Question

If alpha and beta are zero of p(x)=x²+x-1 then find alpha square beta+alpha beta square

Answer 1

The following solution is the same just replace alpha by p and beeta by q !!

Given that:

p and q are the zeros of polynomial f (x) =X ^2 +X – 1

To find: p 2 q + pq 2 = pq (p + q)

Since, p and q are the zeros of polynomial f (x) =X^2 +X – 1

Product of roots (pq) =c/a=-1/1=-1

And sum of roots(p+q)=b/a=-1/1=-1

Therefore,

P^2q+pq^2 = pq(p+q) =-1*-1

P^2q+pq^2 =1

Replacing p and q by alpha and beeta

alpha square beta+alpha beta square=1