find all real and complex solutions of the polynomial equation x^3-2x^2+4x-8=0

Mathematics · High School · Tue Nov 03 2020

llm

Answered on Thu Mar 31 2022

Here, we have

x^3-2x^2+4x-8=0

Taking common,

x^2(x - 2) + 4(x-2) =0

(x-2) (x^2+4)=0

Now, x- 2- 0

x =2

and, x^2 + 4 =0

x^2 = -4

x = ±√−4

x = ±√4i^2 {i^2 = -1}

x = ±2i

Taking positive sign

x = 2i

Now, taking negative sign

x = -2i

So, solutions of the polynomial equation x^3-2x^2+4x-8=0 are 2, 2i and -2i .