Question

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

Answer 1

`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`