Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 8 - Mid-Chapter Check Point - Page 630: 20

Answer

The value of the discriminant of the given equation is $\sqrt{25}$, which is $>0$. Therefore, there are two unequal real solutions that will be obtained.

Work Step by Step

Simplify $10x(x + 4) = 15x - 15$: $10x^2+40x=15x-15$ Add $15$ to both sides. $10x^2+40x+15=15x-15+15$ $10x^2+40x+15=15x$ Subtract $15x$ from both sides. $10x^2+40x+15-15x=15x-15x$ $10x^2+25x+15=0$ Compute for the discriminant. $a=10$, $b=25$, $c=15$ $b^2-4ac = 25^2-(4⋅10⋅15)$ $b^2-4ac = \sqrt {25}$ Note that the discriminant tells the number and types of solution. If: $b^2-4ac > 0$: Two unequal real solutions $b^2-4ac = 0$: One solution (a repeated solution) that is a real number $b^2-4ac < 0$: No real solution; two imaginary solutions The value of the discriminant of the given equation is $\sqrt{25}$, which is $>0$. Therefore, there are two unequal real solutions that will be obtained.
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