Question

if alpha and beta are the zeroes of the quadratic polynomial p(x)=x²+2x-k such that
${ \alpha }^{2} + { \beta }^{2} = 34$
then find the value of k​

Answer 1

alpha+beta=-b/a

alpha+beta=-2

alpha*beta=c/a

alpha*beta=-k

now,

alpha^2+beta^2=34

using identity we get

(alpha+beta)^2-2alpha*beta

now putting up the values

(-2)^2-2*-k=34

4+2k=34

2k=30

k=15

hope you will get!!