Question

The sum of the cubes of all the roots of the equation x⁴ – 3x³ – 2x² + 3x + 1 = 0 is ______.

Answer 1

Answer is 36

x⁴ – 3x³ – 2x² + 3x + 1 = 0 

x = 0 is not the root of this equation so divide it by x²

α³ + ß³ + γ³ + δ³

= 1 - 1 + (γ + δ) ((γ + δ)² - 3γδ)

0 + 3(9 - 3(-1)) 

= 3(12)

 = 36