A partial solution set is given for the polynomial equation. Find the complete solution set.

Question

3x^3-x^2+x-3=0; {1}

Answer 1

Well since 1 is a solution, because 3(1)^3 - 1^2 + 1 - 3 = 3(1) - 1 + 1 - 3 = 3 - 1 + 1 - 3 = 0,

it is factored out using synthetic division

1 | 3 -1 1 -3

3 2 3

____________________

3 2 3 0

So the quadratic equation is factored as (x-1)(3x^2 + 2x + 3)

Quadratic formula says

x = [-2 +or- sqrt ( 2^2 - 4(3)(3))] / [(2)(3)]

= [-2 +or- sqrt ( 4 - 36)] / 6

= [ -2 +or- sqrt(-32)]/ 6

= [ -2 +or- sqrt( -1 * 16 * 2)]/6

= [ -2 +or- 4i*sqrt(2)]/6

[ -1 +or- 2i*sqrt(2)]/3