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: 18


$x=\displaystyle \frac{5+\sqrt{13}}{6}\approx 1.434$ or $x=\displaystyle \frac{5-\sqrt{13}}{6}\approx 0.232$

Work Step by Step

$3x^{2}-5x+1=0$ To factor the trinomial we search for factors of $3\times 1$ whose sum is $-5$ ... ... none We can always use the quadratic formula: (For $ax^{2}+bx+c=0,\ x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ ) $x=\displaystyle \frac{-(-5)\pm\sqrt{(-5)^{2}-4(3)(1)}}{2(3)}$ $x=\displaystyle \frac{5\pm\sqrt{25-12}}{6}$ $x=\displaystyle \frac{5+\sqrt{13}}{6}$ or $x=\displaystyle \frac{5-\sqrt{13}}{6}$ $x\approx 1.434$ or $x\approx 0.232$
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