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: 83

Answer

The equation has one rational solution.

Work Step by Step

$x^{2}-8x+16=0$ The discriminant is given by $b^{2}-4ac$. For this equation, $a=1$, $b=-8$ and $c=16$ Let the discriminant be $D$. Substitute the known values into the formula and evaluate: $D=(-8)^{2}-4(1)(16)=64-64=0$ Since the discriminant is equal to $0$, the equation has only one solution and it is a rational number.
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