Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Appendix A - A.4 - Quadratic Equations - Exercises - Page 556: 25

Answer

$x=2~$ or $~x=4$

Work Step by Step

Let's consider a trinomial in this form: $~x^2+bx+c$ To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = b$ and $r\times s = c$ Then we can factor the trinomial as follows: $~x^2+bx+c = (x+r)~(x+s)$ Let's consider this equation: $~x^2-6x+8=0$ To factor the left side of the equation, we need to find two numbers $r$ and $s$ such that $r+s = -6$ and $r\times s = 8$. We can see that $(-4)+(-2) = -6~$ and $(-4)\times (-2) = 8$ We can solve the equation as follows: $x^2-6x+8=0$ $(x-4)(x-2)=0$ $x=4~$ or $~x=2$
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