Discriminant of the equation `-3x^(2)+2x-8=0` is :

Options

A. `-92`
B. `-29`
C. 39
D. 49

Answer

To find the discriminant of the quadratic equation \(-3x^2 + 2x - 8 = 0\), we will follow these steps:

### Step 1: Identify the coefficients
The standard form of a quadratic equation is \(Ax^2 + Bx + C = 0\). Here, we can identify:
- \(A = -3\)
- \(B = 2\)
- \(C = -8\)

### Step 2: Write the formula for the discriminant
The formula for the discriminant \(D\) of a quadratic equation is given by:
\[ D = B^2 - 4AC \]

### Step 3: Substitute the values into the formula
Now, we will substitute the values of \(A\), \(B\), and \(C\) into the discriminant formula:
\[ D = (2)^2 - 4 \cdot (-3) \cdot (-8) \]

### Step 4: Calculate \(B^2\)
Calculating \(B^2\):
\[ (2)^2 = 4 \]

### Step 5: Calculate \(4AC\)
Now, calculate \(4AC\):
\[ 4 \cdot (-3) \cdot (-8) = 4 \cdot 3 \cdot 8 = 96 \]

### Step 6: Substitute back into the discriminant formula
Now substitute back into the discriminant formula:
\[ D = 4 - 96 \]

### Step 7: Simplify the expression
Now simplify the expression:
\[ D = 4 - 96 = -92 \]

### Conclusion
The discriminant of the equation \(-3x^2 + 2x - 8 = 0\) is \(-92\).

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