The slope of normal to be parabola `y = (x^(2))/(4) -2` drawn through the point `(10,-1)` is (a) -2 (b) `-sqrt(3)` (c) `-1/2` (d) `-5/3`

Options

A. `-2`
B. `-sqrt(3)`
C. `-1//2`
D. `-5//3`

Explanation

To find the slope of the normal to the parabola \( y = \frac{x^2}{4} - 2 \) drawn through the point \( (10, -1) \), we can follow these steps:

### Step 1: Rewrite the equation of the parabola
The given equation of the parabola is:
\[ y = \frac{x^2}{4} - 2 \]
This can be rewritten in standard form:
\[ x^2 = 4y + 8 \]

### Step 2: Identify the value of \( a \)
In the standard form \( x^2 = 4ay \), we can compare:
\[ 4a = 4 \implies a = 1 \]

### Step 3: Write the equation of the normal
The equation of the normal to the parabola at a point \( (x_0, y_0) \) is given by:
\[ x = m(y - 2a) - a m^3 \]
Substituting \( a = 1 \):
\[ x = m(y - 2) - m^3 \]
This simplifies to:
\[ x = my - 2m - m^3 \]

### Step 4: Substitute the point \( (10, -1) \)
We know the normal passes through the point \( (10, -1) \). Substituting these values into the equation:
\[ 10 = m(-1 - 2) - m^3 \]
This simplifies to:
\[ 10 = m(-3) - m^3 \]
or:
\[ 10 = -3m - m^3 \]
Rearranging gives us:
\[ m^3 + 3m + 10 = 0 \]

### Step 5: Solve the cubic equation
We can use the trial and error method to find a root of the cubic equation \( m^3 + 3m + 10 = 0 \). Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 - 6 + 10 = -4 \quad (\text{not a root}) \]
Testing \( m = -1 \):
\[ (-1)^3 + 3(-1) + 10 = -1 - 3 + 10 = 6 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 - 6 + 10 = -4 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Finally, testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]
Testing \( m = -2 \):
\[ (-2)^3 + 3(-2) + 10 = -8 + 6 + 10 = 8 \quad (\text{not a root}) \]

### Conclusion
The slope of the normal to the parabola at the given point is \( m = -2 \).

Thus, the correct answer is:
\[ \text{(a) } -2 \]