## Calculus with Applications (10th Edition)

$x=\displaystyle \frac{5+\sqrt{13}}{6}\approx 1.434$ or $x=\displaystyle \frac{5-\sqrt{13}}{6}\approx 0.232$
$3x^{2}-5x+1=0$ 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 $x\approx 0.232$