Question

How do you find all the real and complex roots of `f(x)=x^3-5x^2+11x-15`?

Answer 1

`x_1=3`, `x_2=1-2i` and `x_3=1+2i`

Explanation:

`x^3-5x^2+11x-15=0`

`x^3-3x^2-2x^2+6x+5x-15=0`

`x^2*(x-3)-2x*(x-3)+5*(x-3)=0`

`(x-3)*(x^2-2x+5)=0`

From first multiplier, `x_1=3`. From second one `x_2=1-2i` and `x_3=1+2i`