Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 5 Polynomials and Polynomial Functions - 5.2 Evaluate and Graph Polynomial Functions - 5.2 Exercises - Mixed Review - Page 344: 66


$-9 \lt z \lt 4$

Work Step by Step

Given: $x^2+5x-36\lt0$ Let the equation equal 0: $x^2+5x-36=0$ $a=1, b=5, c=-36$ Find $x$ by using: $x=\frac{-b \pm \sqrt b^2-4ac}{2a}=\frac{-5\pm\sqrt 5^2-4.1.(-36)}{2.1}=\frac{-5\pm13}{2}$ $x=\frac{-5+13}{2}$ or $x=\frac{-5-13}{2}$ $x=4$ or $x=-9$ Since $a \gt 0$ and the inequality sign is $\lt$, the solution region is below and not including the dashed boundary line. Hence, the solution is $-9 \lt z \lt 4$.
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