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

1 Answer
Jan 26, 2018

Imaginary Roots , (-1+-sqrt(23)i)/(-6)

Explanation:

Simply this equation to get : y=ax^2+bx+c

y=-x^2-3x-2(x^2-2x+1)
y=-x^2-3x-2x^2+4x-2

y=-3x^2+x-2

comparing with: y=ax^2+bx+c

we get a=-3 , b=1, c=-2

using the quadratic formula:

(-b+-sqrt(b^2-4ac))/(2a)
(-1+-sqrt(1^2-4(-3)(-2)))/(2(-3)

Solve further and get
answer = (-1+-sqrt(23)i)/(-6)