Question

What are the potential roots of f(x)=2x2+2x-24

Answer 1

Answer: x = 3, and x = -4

Explanation:

The roots of a quadratic equation can be found by setting the equation equal to zero and solving for x. In this case, we have the equation f(x) = 2x^2 + 2x - 24.

To find the roots, we need to set f(x) equal to zero:

2x^2 + 2x - 24 = 0.

Now, we can solve this equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the roots are given by:

x = (-b ± √(b^2 - 4ac)) / (2a).

In our equation, a = 2, b = 2, and c = -24. Plugging these values into the quadratic formula, we get:

x = (-2 ± √(2^2 - 4(2)(-24))) / (2(2)).

Simplifying the expression inside the square root:

x = (-2 ± √(4 + 192)) / 4,

x = (-2 ± √196) / 4,

x = (-2 ± 14) / 4.

Now we have two possible values for x:

x1 = (-2 + 14) / 4 = 12/4 = 3,

x2 = (-2 - 14) / 4 = -16/4 = -4.

Therefore, the potential roots of f(x) = 2x^2 + 2x - 24 are x = 3 and x = -4.

Answer 2

±{1/2, 1, 3/2, 2, 3, 4, 6, 8, 12, 24}

Explanation:

You want to know the potential roots of f(x) = 2x² +2x -24.

Rational root theorem

The rational root theorem tells you the magnitude of the potential roots will be in the set ...

(divisor of constant)/(divisor of leading coefficient)

That is, they are ...

±{1, 2, 3, 4, 6, 8, 12, 24} ÷ {1, 2}

The potential rational roots are ±{1/2, 1, 3/2, 2, 3, 4, 6, 8, 12, 24}.

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Additional comment

The product of the roots must be -24/2 = -12. The sum of the roots must be -2/2 = -1. The roots that satisfy these criteria are -4 and 3.

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