# How do you find the roots, real and imaginary, of y= -2x^2 + 5x + 72  using the quadratic formula?

May 12, 2018

color(maroon)("Two roots are " x = (5 + sqrt(601)) / 4, (5 - sqrt(601)) / 4

#### Explanation:

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

$\text{Given } y = - 2 {x}^{2} + 5 x + 72$

$= - 2 , b = 5 , c = 72$

$x = \frac{- 5 \pm \sqrt{25 + \left(4 \cdot 2 \cdot 72\right)}}{2 \cdot - 2}$

$x = \frac{- 5 \pm \sqrt{601}}{-} 4$

color(maroon)(x = (5 +- sqrt(601)) / 4