Question

The sin q and cosq 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 q + cos q = –$\frac{m}{\mathcal{l}}$ …(1)

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

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

Ž sin² q + cos²q + 2 sin q cos q =$\frac{m^{2}}{\mathcal{l}^{2}}$

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

Ž l² + 2nl = m²

Ž l² – m² + 2nl = 0