Question

If the equation x² + 5kx + 16 = 0 has no real roots, then:

Options

• `k > 8/5`

• `k < -8/5`

• `-8/5 < k < 8/5`

• none of these

Answer 1

`bb(-8/5 < k < 8/5)`

Explanation:

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

⇒ `k^2 < 64/25`

⇒ `|k| < sqrt(64/25)`

⇒ `|k| < 8/5`

⇒ `-8/5 < k < 8/5`