which equation is true for x = -6 and x = 2?\n2x² - 16x + 12 = 0\n2x² + 8x - 24 = 0\n3x² - 4x - 12 = 0\n3x²…

Explanation:

Step1: Substitute x = -6 into the first equation

Substitute (x=-6) into (2x^{2}-16x + 12): [ \begin{align*} 2\times(-6)^{2}-16\times(-6)+12&=2\times36 + 96+12\ &=72+96 + 12\ &=180\neq0 \end{align*} ]

Step2: Substitute x = -6 into the second equation

Substitute (x = - 6) into (2x^{2}+8x - 24): [ \begin{align*} 2\times(-6)^{2}+8\times(-6)-24&=2\times36-48 - 24\ &=72-48-24\ &=0 \end{align*} ]

Step3: Substitute x = 2 into the second equation

Substitute (x = 2) into (2x^{2}+8x - 24): [ \begin{align*} 2\times2^{2}+8\times2-24&=2\times4 + 16-24\ &=8 + 16-24\ &=0 \end{align*} ]

Step4: Check other equations briefly

For (3x^{2}-4x - 12), when (x=-6), (3\times(-6)^{2}-4\times(-6)-12=3\times36 + 24-12=120\neq0). For (3x^{2}+12x + 36), when (x = 2), (3\times2^{2}+12\times2+36=3\times4+24 + 36=60\neq0).

Answer:

B. (2x^{2}+8x - 24 = 0)