Question

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

Answer 1

The correct answer is 36
x4 – 3x3 – x2 – x2 + 3x + 1 = 0
(x2 – 1) (x2 – 3x – 1) = 0
Let the root of x2 – 3x – 1 = 0 be α and β and other two roots of given equation are 1 and –1
So sum of cubes of roots = 13 + (–1)3 + α3 + β3
= (α + β)3 – 3αβ(α + β)
= (3)3 – 3(–1)(3)
= 36