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: 87

Answer

The equation has two irrational solutions.

Work Step by Step

$4x^{2}=-6x+3$ Take all terms to the left side: $4x^{2}+6x-3=0$ The discriminant is given by $b^{2}-4ac$. For this equation, $a=4$, $b=6$ and $c=-3$ Let the discriminant be $D$. Substitute the known values into the formula and evaluate: $D=6^{2}-4(4)(-3)=36+48=84$ Since the discriminant is equal to a positive, non-perfect square number, the equation has two solutions and they are irrational numbers.
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