Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.5 Quadratic Equations - Concept and Vocabulary Check - Page 399: 14

Answer

False

Work Step by Step

Consider the expression \[{{x}^{2}}+x+20\] where,\[a=1,\ b=1,\text{ and }c=20\] The solution of this quadratic expression can be determined by the quadratic formula\[\begin{align} & x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a} \\ & =\frac{-1\pm \sqrt{1-4\times 1\times 20}}{2} \\ & =\frac{-1\pm \sqrt{1-80}}{2} \\ & =\frac{-1\pm \sqrt{-79}}{2} \end{align}\] The solution is a complex number. Therefore, the given statement is false.
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