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
-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.