Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 4 - Quadratic Functions and Equations - 4-8 Complex Numbers - Practice and Problem-Solving Exercises - Page 254: 62

Answer

$\text{sum:}$ $ -\dfrac{2}{5} $ $\text{product:}$ $ \dfrac{1}{5}$

Work Step by Step

In $ax^2+bx+c=0,$ the sum of the roots is given by $-\dfrac{b}{a}$ while the product of the roots is given by $\dfrac{c}{a}$. In the given quadratic equation, \begin{align*} 5x^2+2x+1=0 ,\end{align*} $a= 5 ,$ $b= 2 ,$ and $c= 1 .$ Using the sum and product ratios of quadratic equations, then \begin{align*}\require{cancel} \text{Sum: }\\-\dfrac{b}{a}&=- \dfrac{2}{5} \\\\ \text{Product: }\\\dfrac{c}{a}&= \dfrac{1}{5} .\end{align*} Hence, $ \text{the sum is }$ $ -\dfrac{2}{5} $ $\text{ and the product is }$ $ \dfrac{1}{5} $.
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