# How do you find the roots, real and imaginary, of y=-6x^2 + 24x +24(x/2-1)^2  using the quadratic formula?

Dec 7, 2017

No roots

#### Explanation:

First,we need to get this equation into Standard Form

$y = - 6 {x}^{2} + 24 x + 24 {\left(\frac{x}{2} - 1\right)}^{2}$

$y = - 6 {x}^{2} + 24 x + 24 \left({x}^{2} / 4 - x + 1\right)$

$y = \cancel{- 6 {x}^{2}} + \cancel{24 x} + \cancel{6 {x}^{2}} - \cancel{24 x} + 24$

$y = 24$

Well, I guess we don't need to use any quadratic formula for this

There are no roots for this, see

graph{y=24x/x}

It never crosses the $x -$axis