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

Explanation:

Step1: Test \( x = 2 \) and \( x = -2 \) in \( x^2 - 4 = 0 \)

For \( x = 2 \): \( 2^2 - 4 = 4 - 4 = 0 \). For \( x = -2 \): \( (-2)^2 - 4 = 4 - 4 = 0 \). So this equation holds.

Step2: Test \( x = 2 \) and \( x = -2 \) in \( x^2 = -4 \)

For \( x = 2 \): \( 2^2 = 4
eq -4 \). For \( x = -2 \): \( (-2)^2 = 4
eq -4 \). So this equation does not hold.

Step3: Test \( x = 2 \) and \( x = -2 \) in \( 3x^2 + 12 = 0 \)

For \( x = 2 \): \( 3(2)^2 + 12 = 3(4) + 12 = 12 + 12 = 24
eq 0 \). For \( x = -2 \): \( 3(-2)^2 + 12 = 3(4) + 12 = 24
eq 0 \). So this equation does not hold.

Step4: Test \( x = 2 \) and \( x = -2 \) in \( 4x^2 = 16 \)

For \( x = 2 \): \( 4(2)^2 = 4(4) = 16 \). For \( x = -2 \): \( 4(-2)^2 = 4(4) = 16 \). So this equation holds.

Step5: Test \( x = 2 \) and \( x = -2 \) in \( 2(x - 2)^2 = 0 \)

For \( x = 2 \): \( 2(2 - 2)^2 = 2(0)^2 = 0 \). For \( x = -2 \): \( 2(-2 - 2)^2 = 2(-4)^2 = 2(16) = 32
eq 0 \). So this equation does not hold.

Answer:

A. \( x^2 - 4 = 0 \), D. \( 4x^2 = 16 \)