132k views
2 votes
What are the potential roots of f(x)=2x2+2x-24

User GKelly
by
8.3k points

2 Answers

3 votes

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.

User Izbassar Tolegen
by
8.2k points
2 votes

Answer:

±{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}.

__

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.

<95141404393>

User Actual
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories