Question

For what m ∈ R, the expression 2x² + mxy + 3y² – 5y – 2 can be expressed as (λx + μy + ν) (px + qy + r) ? Then value of m is –

• A. 5, – 5
• B. 7, – 7
• C. 3, – 3
• D. None of these

Answer 1

Answer: (B)

7, – 7

Answer 2

Condition : abc + 2fgh – af² – bg² – ch² = 0

a = 2, b = 3, h = $\frac{m}{2}$, c = (– 2) f = $\frac{- 5}{2}$, g = 0

⇒ 2.3 (– 2) + 2 $\left( \frac{- 5}{2} \right)$0.

$\frac{m}{2}$– 2 $\left( \frac{- 5}{2} \right)^{2}$– 3.(0)² – (– 2) $\left( \frac{m}{2} \right)^{2}$= 0

m² = 49

m = ± 7