How do you find the roots, real and imaginary, of #y=(2x-8)(x-2)-x^2+4x # using the quadratic formula?

1 Answer
May 7, 2017

Answer:

The roots are #x=4" "or" "x=5/2#

Explanation:

#y=(2x-8)(x-2)-x^2+4x#
#" "#
#y=(2x-8)(x-2)-x(x-4)#
#" "#
#y=(2xxx-2xx4)(x-2)-(x-4)#
#" "#
#y=(2(x-4))(x-2)-(x-4)#
#" "#
#y=2(x-4)(x-2)-(x-4)#
#" "#
#y=(x-4)[2(x-2)-1]#
#" "#
#y=(x-4)[2x-4-1]#
#" "#
#y=(x-4)(2x-5)#
#" "#
We will find the roots when #y=0#
#" "#
#y=0#
#" "#
#rArr(x-4)(2x-5)=0#
#" "#
#x-4=0" "rArrx=4#
#" "#
#" "#OR
#2x-5=0rArr2x=5rArrx=5/2#
#" "#
The roots are #x=4" "or" "x=5/2#