College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 1 - Section 1.4 - Quadratic Equations - 1.4 Exercises: 98

Answer

$a=1, b=0, \text { and } c=1$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the fact that a quadratic equation with roots $r_1$ and $r_2$ has a factored form of $(x-r_1)(x-r_2)=0$. Then use the FOIL Method to convert the equation in the form $ax^2+bx+c=0.$ $\bf{\text{Solution Details:}}$ The factored form of the quadratic equation with the given roots $\{ i,-i \},$ is \begin{array}{l}\require{cancel} (x-i)(x-(-i))=0 \\\\ (x-i)(x+i)=0 .\end{array} Using the product of the sum and difference of like terms which is given by $(a+b)(a-b)=a^2-b^2,$ the expression above is equivalent \begin{array}{l}\require{cancel} (x)^2-(i)^2=0 \\\\ x^2-i^2=0 .\end{array} Since $i^2=-1$, the expression above becomes \begin{array}{l}\require{cancel} x^2-(-1)=0 \\\\ x^2+1=0 .\end{array} Hence, $ a=1, b=0, \text { and } c=1 .$
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