The quadratic equation is x2−kx+k=0. One root exceeds the other by 2√3. ⇒α−β=2√3. Also, Sum of roots: α+β=k Product of roots: α×β=k Calculation: We know the following identity (α+β)2=(α−β)2−4αβ ⇒k2=(2√3)2−4k ⇒k2−12−4k=0 ⇒k2−6k+2k−12=0 ⇒k(k−6)+2(k−6)=0 ⇒(k−6)(k+2)=0 ⇒k=6 and k=−2 Thus, the possible values of k are 6 and -2