Question

If a and B are the zeroes of the polynomial x2-px+q, then find the values of a2+B2.

Answer 1

solution:-
because a & b are the zeroes of polynomial x2-px+q.......
then (a+b)= -(-p)= p...
(ab)= q
so..... (a2+b2)= (a+b)^2 - 2ab
=p^2 - 2q

Answer 2

Hi there !!

p(x) = x² - px + q
a = 1
b = p
c = q

If α and β are the zeroes of p(x) , then :-

α + β = -b/a  = -(-p) = p
αβ = c/a = q

to find :-
α² + β²

α² + β² = (α+ β)² - 2αβ
            = p² - 2q

∴
α² + β² = p² - 2q