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

Answer:

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)#