How do you find the roots, real and imaginary, of y=-5x^2 +40x -34  using the quadratic formula?

Jan 26, 2016

$4 \pm \sqrt{9.2}$

Explanation:

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

with a=-5, b=40 and c=-34 for this particular equation

$\frac{- 40 \pm \sqrt{{40}^{2} - 4 \cdot \left(- 5\right) \left(- 34\right)}}{2 \cdot \left(- 5\right)}$, which gives:

$\frac{- 40 \pm \sqrt{1600 - 680}}{- 10}$,

$\frac{- 40 \pm \sqrt{920}}{- 10}$,

$\frac{40 \pm \sqrt{920}}{10}$,

As 920 is not a perfect square, you can symplify the expression in several ways

$\frac{40 \pm \sqrt{4 \cdot 230}}{10} = \frac{20 \pm \sqrt{230}}{5} = 4 \pm \sqrt{9.2}$