Question

If α and β are the zeroes of the polynomial of the quadratic polynomial p(x) x^2-ax+b, then find the value of α^2+β^2

Answer 1

p(x) = x^2 - ax + b

Alpha + Beta = a
and Alpha*Beta = b

Alpha^2 + Beta^2
= ( alpha + beta)^2 - 2 alpha * beta
= ( a)^2 - 2 b
= a^2 - 2b

Answer 2

$(\alpha + \beta )^{2} - 2 \alpha \beta$

alpha + beta= a
alpha× beta= b
so answer will be a^2-2b