Question

For the quadratic equation 5x2+16x−16=0
, complete the table by testing each of the given values to determine whether it is a solution. Select the appropriate response.(3 points)
Is a solution Is not a solution
-4


4


0

Answer 1

To determine whether each given value is a solution to the quadratic equation \(5x^2 + 16x - 16 = 0\), we will substitute each value into the equation and see if it equals zero.

1. **For \(x = -4\)**:
\[
5(-4)^2 + 16(-4) - 16 = 5(16) - 64 - 16 = 80 - 64 - 16 = 0
\]
- Since the equation equals 0, **-4 is a solution**.

2. **For \(x = 4\)**:
\[
5(4)^2 + 16(4) - 16 = 5(16) + 64 - 16 = 80 + 64 - 16 = 128
\]
- Since the equation does not equal 0, **4 is not a solution**.

3. **For \(x = 0\)**:
\[
5(0)^2 + 16(0) - 16 = 0 + 0 - 16 = -16
\]
- Since the equation does not equal 0, **0 is not a solution**.

Now, we can fill in the table:

| Value | Is a solution | Is not a solution |
|-------|---------------|-------------------|
| -4 | ✅ | |
| 4 | | ✅ |
| 0 | | ✅ |

**Final responses**:
- **-4** is a solution.
- **4** is not a solution.
- **0** is not a solution.