Question

If sinα, sinβ and cosα are in G.P, then roots of the equation

x² + 2x cot β+ 1 = 0 are always

• A. Equal
• B. Real
• C. Imaginary
• D. Greater than 1

Answer 1

Answer: (B)

Real

Answer 2

sinα, sinβ, cosα are in G.P.

⇒ sin²β = sinα cosα

⇒ cos2β = 1 – sin2α ≥ 0

Now, the discriminant of the given equation is

4cot²β – 4 = 4 cos2β ⋅ cosec²β ≥ 0

⇒ Roots are always real