Find the roots of `x^2+3x-4=0` is

Options

A. `1,-4`
B. `3,7`
C. `-1,4`
D. `-5,2`

Answer

To find the roots of the quadratic equation \( x^2 + 3x - 4 = 0 \), we can use the factorization method. Here are the steps:

### Step 1: Write the equation
We start with the equation:
\[ x^2 + 3x - 4 = 0 \]

### Step 2: Factor the quadratic
We need to factor the quadratic expression. We look for two numbers that multiply to \(-4\) (the constant term) and add to \(3\) (the coefficient of \(x\)). The numbers that satisfy these conditions are \(4\) and \(-1\).

Thus, we can rewrite the equation as:
\[ x^2 + 4x - 1x - 4 = 0 \]

### Step 3: Group the terms
Now, we group the terms:
\[ (x^2 + 4x) + (-1x - 4) = 0 \]

### Step 4: Factor by grouping
Next, we factor out the common terms in each group:
\[ x(x + 4) - 1(x + 4) = 0 \]

### Step 5: Factor out the common binomial
Now we can factor out the common binomial \((x + 4)\):
\[ (x + 4)(x - 1) = 0 \]

### Step 6: Set each factor to zero
Now, we set each factor equal to zero:
1. \(x + 4 = 0\)
2. \(x - 1 = 0\)

### Step 7: Solve for \(x\)
Solving these equations gives us:
1. \(x = -4\)
2. \(x = 1\)

### Conclusion
Thus, the roots of the equation \(x^2 + 3x - 4 = 0\) are:
\[ x = 1 \quad \text{and} \quad x = -4 \]