Question

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

Answer 1

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

Explanation:

Multiply out the bracket:
`y=-(4x^2-4x+1)+3x^2-2`
`y=-4x^2+4x-1+3x^2-2`
`y=-x^2+4x-3`

Apply the quadratic formula `(-b+-sqrt(b^2-4ac))/(2a)`:
`(-4+-sqrt(16-4*3))/(-2)=(-4+-2)/(-2)=2+-1=1,3`