Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 4 - Quadratic Functions - 4.5 Solving Equations by Factoring - 4.5 Exercises - Page 359: 34

Answer

Amelia was wrong because she did not write the equation in the form $x^2+bx+c=0$ . The solution set is $\left\{0, \frac{3}{2}\right\}$.

Work Step by Step

Amelia was wrong because she did not write the equation in the form $x^2+bx+c=0$ before factoring. The Zero-Product Property can only be used for equations in the form $ab=0$. The correct work is the one below: \begin{align*} 4x^2-6x&=0\\ 2x(2x-3)&=0\\ 2x&=0 &\text{or}& &2x-3=0\\ x&=0 &\text{or}& &x=\frac{3}{2}\end{align*}
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