If `8 and -4` are the solutions for x, which of the following could be the equation?

Options

A. `x^2 - 4x - 32 = 0`
B. `x^2 - 4x + 32 = 0`
C. `x^2 + 4x - 12 = 0`
D. `x^2 + 4x + 32 = 0`

Answer

To find the quadratic equation with the solutions \(8\) and \(-4\), we can follow these steps:

### Step 1: Write the factors based on the solutions
Since the solutions of the quadratic equation are \(x = 8\) and \(x = -4\), we can express the factors of the equation as:
\[ (x - 8) \quad \text{and} \quad (x + 4) \]

### Step 2: Form the equation
To form the quadratic equation, we multiply the factors:
\[ (x - 8)(x + 4) = 0 \]

### Step 3: Expand the equation
Now, we will expand the product:
\[ x^2 + 4x - 8x - 32 = 0 \]

### Step 4: Combine like terms
Next, we combine the like terms:
\[ x^2 + (4x - 8x) - 32 = 0 \]
This simplifies to:
\[ x^2 - 4x - 32 = 0 \]

### Conclusion
Thus, the quadratic equation that has \(8\) and \(-4\) as solutions is:
\[ x^2 - 4x - 32 = 0 \]