How do you find the roots, real and imaginary, of #y=-3x^2 -6x+4(x -1)^2 # using the quadratic formula?

1 Answer
Oct 31, 2017

Answer:

#color(magenta)(x=7+3sqrt5#

or#color(magenta)(x=7-3sqrt5#

Explanation:

If the question excludes the"y=" then:-

#:.-3x^2-6x+4(x-1)^2#

#:.=-3x^2-6x+4(x^2-2x+1)#

#:.=-3x^2-6x+4x^2-8x+4#

#:.=x^2-14x+4#

#:.x=(-b+-sqrt(b^2-4ac))/(2a)#

#:.x=(-(-14)+-sqrt((-14)^2-4(1)(4)))/(2(1))#

#:.x=(14+-sqrt(196-16))/2#

#:.x=(14+-sqrt180)/2#

#:.x=(14+-sqrt(2*2*3*3*5))/2#

#:.x=(14+-6sqrt5)/2#

#:.x=cancel14^7/cancel2^1+-cancel6^3sqrt5/cancel2^1#

#:.color(magenta)(x=7+3sqrt5# or #color(magenta)(x=7-3sqrt5#