Question

How do you find the roots, real and imaginary, of `y=-5(x-2)^2+3x^2-15` using the quadratic formula?

Answer 1

`color(violet)(x = 5 + sqrt 15, 5 - sqrt15`

Explanation:

`y = -5(x-2)^2 + 3x^2 - 15`

`y = -5x^2 + 20x - 20 + 3x^2 - 15`

`y = -2x^2 + 20x - 35`

`x = (-20 +- sqrt(20^2 - 280)) / -4`

`x = (-20 +- sqrt120) / -4`

`color(violet)(x = 5 + sqrt 15, 5 - sqrt15`