# How do you find the roots, real and imaginary, of y=2x^2 -42x-28  using the quadratic formula?

Jul 4, 2017

$x = \frac{21 \pm \sqrt{497}}{2}$

#### Explanation:

$f \left(x\right) = 2 {x}^{2} - 42 x - 28 = 0$
$f \left(x\right) = 2 \left({x}^{2} - 21 x - 14\right) = 0$
Use the improved quadratic formula in graphic form:
$D = {d}^{2} = {b}^{2} - 4 a c = 441 + 56 = 497$ --> $d = \pm \sqrt{497}$
There are 2 real roots:
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = \frac{21}{2} \pm \frac{\sqrt{497}}{2} = \frac{21 \pm \sqrt{497}}{2}$