If the equation x^2 + 5kx + 16 = 0 has no real roots, then : 1. k > 8/5 2. k < -8/5 3. - 8/5 < k < 8/5 4. none of these

Comparing x2 + 5kx + 16 = 0 with ax2 + bx + c = 0 we get, a = 1, b = 5k and c = 16. We know that, Since equations has no real roots, ⇒ D 0 ⇒ b2 - 4ac 0 ⇒ (5k)2 - 4(1)(16) 0 ⇒ 25k2 - 64 0 ⇒ 25k2 64 Hence, option 3 is the correct option.