Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.7 - Equations - Exercise Set - Page 109: 166

Answer

The statement is false. To make it true, replace "cannot" with "can".

Work Step by Step

EVERY quadratic equation can be solved by the quadratic formula Here,$ b=0$ and $ x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}=\frac{0\pm\sqrt{0-4ac}}{2a}$ $=\displaystyle \frac{\pm 2\sqrt{-ac}}{2a}=\frac{\pm\sqrt{-ac}}{a}$ Solving by the square-root-property method, $ ax^{2}=-c $ $ x^{2}=-\displaystyle \frac{c}{a}$ $ x= \displaystyle \pm\sqrt{\frac{-c}{a}} =\pm\frac{\sqrt{-c}}{\sqrt{a}}\cdot\frac{\sqrt{a}}{\sqrt{a}}$ $=\displaystyle \frac{\pm\sqrt{-ac}}{a}$ (the same solution) The statement is false. To make it true, replace "cannot" with "can".
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