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

**1. For \(x = 0\):**

\[
5(0)^2 + 16(0) - 16 = 0 + 0 - 16 = -16 \quad \text{(not 0)}
\]

**Result:** \(0\) is **not a solution**.

---

**2. For \(x = 4\):**

\[
5(4)^2 + 16(4) - 16 = 5(16) + 64 - 16 = 80 + 64 - 16 = 128 \quad \text{(not 0)}
\]

**Result:** \(4\) is **not a solution**.

---

**3. For \(x = -4\):**

\[
5(-4)^2 + 16(-4) - 16 = 5(16) - 64 - 16 = 80 - 64 - 16 = 0
\]

**Result:** \(-4\) is **a solution**.

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### Summary Table:
- **Is a solution**: \(-4\)
- **Is not a solution**: \(0\), \(4\)