College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Section 1.2 - Quadratic Equations - 1.2 Assess Your Understanding: 45

Answer

The solution set is {$2-\sqrt 5, 2+\sqrt 5$}.

Work Step by Step

$x^2-4x-1=0$ $a=1, b=-4, c=-1$ $D=b^2-4ac=(-4)^2-4\cdot1(-1)=16+4=20>0$ The equation has two real solutions. $x=\frac{-b\pm\sqrt {b^2-4ac}}{2a}=\frac{4\pm\sqrt 20}{2}$ Use quadratic formula. $x=\frac{4\pm2\sqrt 5}{2}$ Simplify $x=2\pm\sqrt 5$ $x=2+\sqrt 5$, $x=2-\sqrt 5$ The solution set is {$2-\sqrt 5, 2+\sqrt 5$}.
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