Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter R - Algebra Reference - R.4 Equations - R.4 Exercises - Page R-16: 20


$\displaystyle \frac{-1+\sqrt{5}}{2}\approx 0.618$ $\displaystyle \frac{-1-\sqrt{5}}{2}\approx-1.618$

Work Step by Step

$p^{2}+p-1=0$ To factor the trinomial we search for integer factors of $-1$ whose sum is $+1$ ... ... none We can always use the quadratic formula: (For $ax^{2}+bx+c=0,\ x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ ) $p=\displaystyle \frac{-1\pm\sqrt{1^{2}-4(1)(-1)}}{2(1)}$ $p=\displaystyle \frac{-1\pm\sqrt{5}}{2}$ Solutions : $\displaystyle \frac{-1+\sqrt{5}}{2}\approx 0.618$ and $\displaystyle \frac{-1-\sqrt{5}}{2}\approx-1.618$.
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