Question

if alpha and beta are the zeros of the quadratic polynomial such that alpha + beta equals to 24 and Alpha minus beta equals to 8 find a quadratic polynomial having alpha and beta its zeros

Answer 1

the given quadratic equation is x2-24x+128

Answer 2

alpha + beta =24......eq 1
alpha - beta = 8........eq 2
on adding eq 1 ,2
we get alpha= 16
substituting alpha in eq 2
16 - beta= 8
beta = 8
alpha + beta = 24
alpha × beta = 16 × 8= 128
quadratic polynomial= x^2-x(alpha + beta) +
(alpha × beta)
quadratic polynomial = x^ 2-x (24)+128
=x^2-24 x +128