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 0 -4 4

Answer 1

To determine if the given values are solutions to the quadratic equation \(5x^2 + 16x - 16 = 0\), we will substitute each value into the equation and check if the equation equals zero.

1. **Testing \(x = 0\):**
\[
5(0)^2 + 16(0) - 16 = 0 + 0 - 16 = -16 \quad (\text{Is not a solution})
\]

2. **Testing \(x = -4\):**
\[
5(-4)^2 + 16(-4) - 16 = 5(16) - 64 - 16 = 80 - 64 - 16 = 0 \quad (\text{Is a solution})
\]

3. **Testing \(x = 4\):**
\[
5(4)^2 + 16(4) - 16 = 5(16) + 64 - 16 = 80 + 64 - 16 = 128 \quad (\text{Is not a solution})
\]

Now, we can summarize the results in the table:

- For **0**: Is not a solution
- For **-4**: Is a solution
- For **4**: Is not a solution

### Final Responses:
- 0: **Is not a solution**
- -4: **Is a solution**
- 4: **Is not a solution**