How do you find the roots of the polynomial #-x^3+5x^2-11x+55=0#?

1 Answer
Jan 12, 2017

Answer:

#x = 5" "# or #" "x = +-sqrt(11)i#

Explanation:

This cubic factors by grouping:

#0 = -x^3+5x^2-11x+55#

#color(white)(0) = (-x^3+5x^2)+(-11x+55)#

#color(white)(0) = -x^2(x-5)-11(x-5)#

#color(white)(0) = -(x^2+11)(x-5)#

#color(white)(0) = -(x^2-(sqrt(11)i)^2)(x-5)#

#color(white)(0) = -(x-sqrt(11)i)(x+sqrt(11)i)(x-5)#

Hence:

#x = 5" "# or #" "x = +-sqrt(11)i#