Question

If the equation x² – kx + 1 = 0 has no real roots then ______.

Options

• k < –2

• k > 2

• –2 < k < 2

• none of these

Answer 1

If the equation x² – kx + 1 = 0 has no real roots then –2 < k < 2.

Explanation:

It is given that the equation x² – kx + 1 = 0 has no real roots. 

∴ (b² – 4ac) < 0 

⇒ (–k)² – 4 × 1 × 1 < 0 

⇒ k² < 4 

⇒ –2 < k < 2