Question

How do you solve this polynomial `2x^3 - 3x^2 + 8x -12 =0` by finding all roots?

Answer 1

Solution: Roots are `x =3/2, x= 2i, x = - 2i`

Explanation:

`2x^3-3x^2+8x-12=0 or x^2(2x-3)+4(2x-3)=0` or

`(2x-3)(x^2+4)=0 :.` either , `2x-3=0 :. x =3/2` or

`x^2+4=0 :. x^2 = -4 :. x = +- sqrt (-4)= +- sqrt (4i^2)` or

`x=+- 2i [i^2=-1] :. (x-3/2)(x-2i)(x+2i)=0`

Solution: Roots are `x =3/2, x= 2i, x = - 2i` [Ans]