# How do you find the roots, real and imaginary, of y=-(2x-1)^2 + 3x^2 - 2  using the quadratic formula?

Jun 15, 2018

Multiply out the bracket and collect terms in order to put it into standard quadratic form

#### Explanation:

Multiply out the bracket:
$y = - \left(4 {x}^{2} - 4 x + 1\right) + 3 {x}^{2} - 2$
$y = - 4 {x}^{2} + 4 x - 1 + 3 {x}^{2} - 2$
$y = - {x}^{2} + 4 x - 3$

Apply the quadratic formula $\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$:
$\frac{- 4 \pm \sqrt{16 - 4 \cdot 3}}{- 2} = \frac{- 4 \pm 2}{- 2} = 2 \pm 1 = 1 , 3$