According to the rational root theorem, the following are potential roots of f(x) = 2x² + 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) = 2x² + 2x - 24

By solving the quadratic equation to determine the roots

2x² + 2x - 24 = 0

Divide the equation by 2

x² + x - 12 = 0

By splitting of the middle terms

x² + 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.

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According to the rational root theorem, the following are potential roots of f(x) = 2x² + 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) = 2x² + 2x - 24.  -4, -3, 2, 3, 4. The actual roots of f(x) are 3 and -4.