# How do you find the roots, real and imaginary, of y=3x^2+5x+2 using the quadratic formula?

Jan 12, 2016

Substitute the coefficients into the quadratic formula to find zeros:

$x = - 1$ and $x = - \frac{2}{3}$

#### Explanation:

$y = 3 {x}^{2} + 5 x + 2$ is of the form $a {x}^{2} + b x + c$ with $a = 3$, $b = 5$ and $c = 2$

It has zeros given by the quadratic formula:

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

$= \frac{- 5 \pm \sqrt{{5}^{2} - \left(4 \cdot 3 \cdot 2\right)}}{2 \cdot 3}$

$= \frac{- 5 \pm \sqrt{25 - 24}}{6}$

$= \frac{- 5 \pm 1}{6}$

That is $x = - 1$ and $x = - \frac{2}{3}$