Question

Which equations are true for x = –2 and x = 2? Select two options

x2 – 4 = 0
x2 = –4
3x2 + 12 = 0
4x2 = 16
2(x – 2)2 = 0

Answer 1

To determine which equations are true for x = -2 and x = 2, let's substitute the values of x into each equation and evaluate:

x^2 - 4 = 0:

For x = -2: (-2)^2 - 4 = 4 - 4 = 0 (True)

For x = 2: (2)^2 - 4 = 4 - 4 = 0 (True)

x^2 = -4:

For x = -2: (-2)^2 = 4 ≠ -4 (False)

For x = 2: (2)^2 = 4 ≠ -4 (False)

3x^2 + 12 = 0:

For x = -2: 3(-2)^2 + 12 = 3(4) + 12 = 12 + 12 = 24 ≠ 0 (False)

For x = 2: 3(2)^2 + 12 = 3(4) + 12 = 12 + 12 = 24 ≠ 0 (False)

4x^2 = 16:

For x = -2: 4(-2)^2 = 4(4) = 16 (True)

For x = 2: 4(2)^2 = 4(4) = 16 (True)

2(x - 2)^2 = 0:

For x = -2: 2(-2 - 2)^2 = 2(-4)^2 = 2(16) = 32 ≠ 0 (False)

For x = 2: 2(2 - 2)^2 = 2(0)^2 = 2(0) = 0 (True)

Based on the evaluations, the two equations that are true for both x = -2 and x = 2 are:

- x^2 - 4 = 0

- 4x^2 = 16

You're welcome! ^^