If ax2+bx+c=0 has no real roots, then Discriminant (D)=b2−4ac<0 Given quadratic equation is (k−3)x2−kx−1 According to the above concept, ⇒b2−4ac<0 ⇒(−k)2−4(k−3)(−1)<0 ⇒k2+4k−12<0 ⇒k2+6k−2k−12<0 ⇒k(k+6)−2(k+6)<0 ⇒(k−2)(k+6)<0 ∴ The required value is −6<k<2.