Question

Find the value of k for which the equation x2 + 5kx + 16 = 0 has no real roots.

Answer 1

Given quadratic equation is x2 + 5kx + 16 = 0 here a = 1, b = 5k and c = 16 Since there are no real roots, b2 – 4ac < 0 That is (5k)2 – 4(1)(16) < 0 ⇒ 25k2 < 64 ⇒ k2 < 64/25⇒ k2 < (8/5)2 That is k < 8/5