ACT Math : Equations / Inequalities

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #51 : Quadratic Equations

Solve: \(\displaystyle x^{2}-5x+6\) 

Possible Answers:

\(\displaystyle -2\) and \(\displaystyle 3\)

\(\displaystyle -2\) and \(\displaystyle -3\)

None of the other answers

\(\displaystyle 2\) and \(\displaystyle -3\)

\(\displaystyle 2\) and \(\displaystyle 3\)

Correct answer:

\(\displaystyle 2\) and \(\displaystyle 3\)

Explanation:

To solve, we must set it equal to zero. The above expression is of the form \(\displaystyle ax^{2}+bx+c\), so we can use the quadratic formula:

\(\displaystyle x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\)

to solve for the roots which are \(\displaystyle 2\) and \(\displaystyle 3\)

We can check by plugging the roots into the expression and making sure that it equals zero.

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