according to the rational root theorem, the following are potential roots of $f(x)=2x^{2}+2x - 24$. -4, -3…

according to the rational root theorem, the following are potential roots of $f(x)=2x^{2}+2x - 24$. -4, -3, 2, 3, 4 which are actual roots of $f(x)$? -4 and 3 -4, 2, and 3 -3 and 4 -3, 2, and 4

according to the rational root theorem, the following are potential roots of $f(x)=2x^{2}+2x - 24$. -4, -3, 2, 3, 4 which are actual roots of $f(x)$? -4 and 3 -4, 2, and 3 -3 and 4 -3, 2, and 4

Answer

Explanation:

Step1: Substitute -4 into f(x)

$f(-4)=2\times(-4)^2 + 2\times(-4)-24=2\times16-8 - 24=32-8 - 24 = 0$

Step2: Substitute -3 into f(x)

$f(-3)=2\times(-3)^2+2\times(-3)-24=2\times9 - 6-24=18-6 - 24=-12\neq0$

Step3: Substitute 2 into f(x)

$f(2)=2\times2^2+2\times2 - 24=2\times4 + 4-24=8 + 4-24=-12\neq0$

Step4: Substitute 3 into f(x)

$f(3)=2\times3^2+2\times3-24=2\times9+6 - 24=18 + 6-24 = 0$

Step5: Substitute 4 into f(x)

$f(4)=2\times4^2+2\times4-24=2\times16+8 - 24=32+8 - 24 = 16\neq0$

Answer:

A. -4 and 3