Given, the equations x2+kx+64=0 and x2−8x+k=0 have real roots, Let D1 be the discriminant of the equations x2+kx+64−0 ⇒D1=k2−4(1)(64) ⇒D1=k2−256 D2 be the discriminant of the given equations x2−8x+k=0 ⇒D2=64−4(k)(1) ⇒D2=64−4k Given, the equation x2+kx+64=0 and x2−8x+k=0 have real roots if D1,D2≥0 ⇒k2−256≥0 and 64−4k≥0 ⇒(k−16)(k+16)≥0 and 64≥4k ⇒k≥16 or k≥−16 and k≤16 But k≥−16 is not posisble ⇒k≥16 and k≤16 ⇒k=16 Hence, if the equations x2+kx+64=0 and x2−8x+k=0 have real roots, then the value of k is 16.