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

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Answer 1 · 2017-04-18T05:38:20

Roots are #(5+isqrt71)4# and #(5-isqrt71)4#

#y=-x^2-x-3-(x-3)^2#

= #-x^2-x-3-(x^2-6x+9)#

= #-x^2-x-3-x^2+6x-9#

= #-2x^2+5x-12#

Using quadratic formula, the roots are #(-5+-sqrt(5^2-4×(-2)×(-12)))/(2×(-2)#

= #(-5+-sqrt(25-96))/(-4)#

= #(5+-sqrt(-71))/4#

i.e. roots are #(5+isqrt71)4# and #(5-isqrt71)4#