ACT Math : How to factor the quadratic equation

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #11 : Quadratic Equations

What are the two solutions to the following quadratic equation? 

\(\displaystyle 3x^{2} - 6x - 24\)

Possible Answers:

\(\displaystyle x=-2\) and \(\displaystyle x=4\)

\(\displaystyle x=2\) and \(\displaystyle x=2\)

\(\displaystyle x=-2\) and \(\displaystyle x=2\)

\(\displaystyle x=-2\) and \(\displaystyle x=-2\)

\(\displaystyle x=-4\) and \(\displaystyle x=2\)

Correct answer:

\(\displaystyle x=-2\) and \(\displaystyle x=4\)

Explanation:

The equation can be factored.

First pull out a common factor of three from each term.

 \(\displaystyle 3x^2 -6x-24 = 3(x^2 -2x -8)\).

Now, find the factors of the constant term that when added together result in the middle term.

\(\displaystyle = 3(x-4)(x+2)\)

The roots are what values will make the equation equal \(\displaystyle 0\).  

Therefore, the answers are \(\displaystyle x=4\) and \(\displaystyle x=-2.\)

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