Question

If sin ∝, sin β and cos∝ are in G.P., then roots of $x^2$ + 2x cot β + 1 = 0 are always :

• A. Real
• B. Imaginary
• C. Real and positive
• D. Real and negative

Answer 1

The correct option is A

Real

$B^2$ -4AC

Then ${\left(2cot\beta \right)}^2$ – 4

4(${cot}^2$β-1)

4 ${tan}^2$β

Here ${tan}^2$β can’t be negative

Therefore 4${tan}^2$β $\ge$ 0

Roots are real