# How do you find all zeros of the function f(x)=3x^2-17x+20?

Mar 12, 2016

Use the quadratic formula to find:

$x = 4$ or $x = \frac{5}{3}$

#### Explanation:

$3 {x}^{2} - 17 x + 20$ is of the form $a {x}^{2} + b x + c$ with $a = 3$, $b = - 17$ and $c = 20$.

This has zeros given by the quadratic formula:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$= \frac{17 \pm \sqrt{{\left(- 17\right)}^{2} - \left(4 \cdot 3 \cdot 20\right)}}{2 \cdot 3}$

$= \frac{17 \pm \sqrt{289 - 240}}{6}$

$= \frac{17 \pm \sqrt{49}}{6}$

$= \frac{17 \pm 7}{6}$

That is $x = 4$ or $x = \frac{5}{3}$