Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.4 Quadratic Equations - 1.4 Exercises - Page 121: 49


Francisco was wrong because the quadratic formula works even when $c=0$.

Work Step by Step

RECALL: The quadratic equation $ax^2+bx+c=0$ can be solved using the quadratic formula: $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ The given equation has: $a=1, b=-8, c=0$ Substitute these values into the quadratic formula to obtain: $x=\dfrac{-(-8) \pm \sqrt{(-8)^2-4(1)(0)}}{2(1)} \\x=\dfrac{8\pm\sqrt{64-0}}{2} \\x=\dfrac{8\pm\sqrt{64}}{2} \\x=\dfrac{8\pm8}{2} \\x_1=\dfrac{8-8}{2}=0 \\x_2=\dfrac{8+8}{2}=8$ Thus, the solution set is $\color{blue}{\left\{0, 8\right\}}$. Francisco was wrong because the quadratic formula actually works for regardless of whether $c=0$ or not.
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