Question

Find the sum of the cubes of the roots of the equation x³ - 6x² + 11x - 6 = 0
1. 31
2. 32
3. 35
4. 36

Answer 1

Correct Answer - Option 4 : 36

Concept:

The general form of a cubic equation is : f(x) = ax³ + bx² + cx + d = 0. And the cubic equation has the form of ax³ + bx² + cx + d = 0, where a , b and c are the coefficients and d is the constant .

Calculation :

Given, x³ - 6x² + 11x - 6 = 0

⇒ (x - 1) is one of the factors.

 By dividing x³ - 6x² + 11x - 6 by (x - 1),

⇒ (x - 1) (x² - 5x + 6) = 0

⇒ (x - 1) (x - 2 ) (x - 3) = 0

This of the cubic equation solution are x = 1, x = 2 and x = 3.

Sum of cubes = A³ + B³ + C³

 A = 1, B = 2 and C = 3

⇒ A³ + B³ + C³ = (1)³ + (2)³ + (3)³

⇒ 1 + 8 + 27

⇒ 36