# 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 the actual roots of f(x)?

4 and 3; 4, 2 and 3; 3 and -4; 3, 2, and 4

**Solution:**

Given:

Function f(x) = 2x^{2} + 2x - 24

**By solving the quadratic equation to determine the roots**

2x^{2} + 2x - 24 = 0

**Divide the equation by 2**

x^{2} + x - 12 = 0

**By splitting of the middle terms**

x^{2} + 4x - 3x - 12 = 0

**Taking out the common terms**

x(x + 4) - 3(x + 4) = 0

(x + 4)(x - 3) = 0

**So we get,**

x + 4 = 0 or x - 3 = 0

x = -4 or x = 3

**Therefore, the actual roots of f(x) are 3 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 the actual roots of f(x)?

**Summary:**

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

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