For the quadratic equation 5x2+16x−16=0

Question

, 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.

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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.

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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: \(0\), \(4\)