# How do you find the roots, real and imaginary, of y=2x^2 + 5x - 12  using the quadratic formula?

Feb 25, 2016

Look at $\left({b}^{2} - \left(4 \times a \times c\right)\right)$ part of the formula.

#### Explanation:

In a quadratic equation the formula to find the roots is

$x = \frac{- b \pm \sqrt{{b}^{2} - \left(4 \times a \times c\right)}}{2 a}$

If $- \sqrt{{b}^{2} - \left(4 \times a \times c\right)}$ is positive, the roots of the given function are real.

If $\left({b}^{2} - \left(4 \times a \times c\right)\right)$ is negative, the roots of the given function are imaginary.

In our case -

(5^2-(4 xx 2 xx (-12)
(25-(-96)
$\left(25 + 96\right) = 121 > 0$

Since $\left({b}^{2} - \left(4 \times a \times c\right)\right) = 121 > 0$ positive, the roots of the given function are real.