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

1 Answer
Feb 17, 2016

Answer:

There are two imaginary roots:
#color(white)("XXX")1/2+sqrt(39)/6i# and #1/2-sqrt(39)/6i#

Explanation:

First expand the expression given on the left into standard form:
#y=x^2-5x-(2x-2)^2#
#color(white)("XXX")y=x^2-5x-(4x^2-8x+4)#

#color(white)("XXX")y=-3x^2+3x-4#

This is in standard form: #y=ax^2+bx+c# for which the quadratic formula tells us the roots are:
#color(white)("XXX")x=(-b+-sqrt(b^2-4ac))/(2a)#

For this specific example, the roots are
#color(white)("XXX")x=(-3+-sqrt(3^2-4(-3)(-4)))/(2(-3)#

#color(white)("XXXX")=(-3+-sqrt(-39))/(-6)#

#color(white)("XXXX")=1/2+-sqrt(39)/6i#