Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 3 - Linear and Quadratic Functions - 3.3 Quadratic Functions and Their Properties - 3.3 Assess Your Understanding - Page 145: 2


$x=\frac{1}{2}$ or $x=-4$

Work Step by Step

Equation:$2x^2+7x-4=0$ Factor the trinomial. The coefficient of $x^2$ is $2$, hence the coefficients of x in the multipliers are probably $2$ and $1$. The coefficient of $x^0$ (the constant) is $-4$, hence the possible coefficients of the $x^0$ are: $-2$ and $2$; or $-1$ and $4$; or $1$ and $-4$. Out of these combinations, the factors that give a middle term of $7x$ are $(2x-1)(x+4)=0$. Use the Zero-Product Property by equating each factor to zero, then solve each equation to obtain: \begin{align*} 2x-1&=0 &\text{or}& &x+4=0\\ 2x&=1 &\text{or}& &x=-4\\ x&=\frac{1}{2} &\text{or}& &x=-4 \end{align*}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.