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 122: 86


The equation has two rational solutions.

Work Step by Step

$8x^{2}=-14x-3$ Take all terms to the left side: $8x^{2}+14x+3=0$ The discriminant is given by $b^{2}-4ac$. For this equation, $a=8$, $b=14$ and $c=3$ Let the discriminant be $D$. Substitute the known values into the formula and evaluate: $D=14^{2}-4(8)(3)=196-96=100$ Since the discriminant is equal to a positive, perfect square number, the equation has two rational solutions and they are rational numbers.
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