College Algebra (10th Edition)

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

Chapter 5 - Section 5.5 - The Real Zeros of a Polynomial Function - 5.5 Assess Your Understanding - Page 386: 4


$\left\{\dfrac{-1-\sqrt{13}}{2}, \dfrac{-1+\sqrt{13}}{2}\right\}$

Work Step by Step

Using the standard form $ax^2+bx+c=0$ as reference, the given quadratic equation has $a=1, b=1, \text{ and } c=-3$. Solve using the Quadratic Formula $x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$ using the values above to obtain: \begin{align*} x&=\frac{-1\pm\sqrt{1^2-4(1)(-3)}}{2(1)}\\\\ &=\frac{-1\pm\sqrt{1+12}}{2}\\\\ &=\frac{-1\pm\sqrt{13}}{2}\\\\ \end{align*} Thus, the solution set is: $\left\{\dfrac{-1-\sqrt{13}}{2}, \dfrac{-1+\sqrt{13}}{2}\right\}$
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