Question

If alpha and beta are the zeros of the quadratic polynomial,f(x) =6x^2+x-2,then find the value of alpha cube +beta cube ?

Answer 1

Step-by-step explanation:

Given -

• α and β are zeroes of polynomial f(x) = 6x² + x - 2

To Find -

• Value of α³ + β³

Now,

→ 6x² + x - 2

By middle term splitt :-

→ 6x² + 4x - 3x - 2

→ 2x(3x + 2) - 1(3x + 2)

→ (2x - 1)(3x + 2)

Zeroes are -

→ 2x - 1 = 0 and 3x + 2 = 0

→ x = 1/2 and x = -2/3

Then, The value of α³ + β³ is

→ (1/2)³ + (-2/3)³

→ 1/8 - 8/27

→ 27 - 64/216

→ -37/216

Hence,

The value of α³ + β³ is -37/216