Question

The sin θ and cosθ are roots of the equation lx² + mx + n = 0, then

• A. l² + m² + 2ln = 0
• B. l² – m² + 2ln = 0
• C. l² – m² – 2ln = 0
• D. None of these

Answer 1

Answer: (B)

l² – m² + 2ln = 0

Answer 2

Here

sin θ + cos θ = –$\frac{m}{\mathcal{l}}$ …(1)

sin θ . cos θ = $\frac{n}{\mathcal{l}}$ …(2)

Squaring (1) (sin θ + cos θ)² =$\frac{m^{2}}{\mathcal{l}^{2}}$

⇒ sin² θ + cos²θ + 2 sin θ cos θ =$\frac{m^{2}}{\mathcal{l}^{2}}$

⇒ 1 + $\frac{2n}{\mathcal{l}}$=$\frac{m^{2}}{\mathcal{l}^{2}}$

⇒ l² + 2nl = m²

⇒ l² – m² + 2nl = 0