# How do you find the roots, real and imaginary, of y=x^2 + 3x + 1  using the quadratic formula?

Dec 23, 2015

#### Answer:

Substitute the coefficients into the formula and evaluate. There are no imaginary roots

#### Explanation:

$y = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$ is the quadratic formula
In this example $a = 1$, $b = 3$ and $c = 1$
$y = \frac{- 3 \pm \sqrt{9 - 4}}{2}$
$y = \frac{- 3 - \sqrt{5}}{2}$ or $y = - \frac{- 3 + \sqrt{5}}{2}$