Question

If the roots of 5x² – kx + 1 = 0 are real and distinct then

Options

• `-2sqrt(5) < k < 2sqrt(5)`

• `k > 2sqrt(5)` only

• `k < -2sqrt(5)` only

• either `k > 2sqrt(5)` or `k < -2sqrt(5)`

Answer 1

`bb(either  k > 2sqrt(5) or k < -2sqrt(5))`

Explanation: 

It is given that the roots of the equation (5x² – k + 1 = 0) are real and distinct.

∴ (b² – 4ac) > 0

⇒ (–k)² – 4 × 5 × 1 > 0 

⇒ k² – 20 > 0 

⇒ k² > 20

⇒ `k > sqrt(20)` or `k < -sqrt(20)` 

⇒ `k > 2sqrt(5)` or `k < -2sqrt(5)`