Given: 2x2−2(k−2)x−(k+1)=0 By comparing the given equation with the quadratic equation, ax2+bx+c=0. We get, a=2,b=−2(k−2) and c=−(k+1) Let alpha and beta be the roots of the equation 2x2−2(k−2)x−(k+1)=0. ⇒α+β=−
−2(k−2)
2
=k−2 ⇒α×β=
−(k+1)
2
As we know that, α2+β2=(α+β)2−2αβ ⇒α2+β2=(k−2)2+(1+k) =k2−4k+4+1+k =k2−3k+5 =k2−2×