Question

if alpha and beta are zeroes of p(x)=x^2-x-1. find the value of alpha cube +beta cube.

Answer 1

Alpha = a & beta = b

Answer:

4

Step-by-step explanation:

Polynomials written in form of x^2 - Sx + P, represent S as sum of roots anf P as product of roots.

So, here,

Sum = a + b = 1

Product = ab = - 1

= > a + b = 1

Cube on both sides -

= > ( a + b )³ = 1³

= > a³ + b³ + 3ab( a + b ) = 1

= > a³ + b³ + 3(product)(sum) = 1

= > a³ + b³ + 3(-1)(1) = 1

= > a³ + b³ - 3 = 1

= > a³ + b³ = 1+ 3

= > a³ + b³ = 4