Find the value of \(k\), if \(2x + y = 0\) is one of the lines represented by \(3x^2 + kxy + 2y^2 = 0\).
Q.6 Find the value of \(k\), if \(2x + y = 0\) is one of the lines represented by \(3x^2 + kxy + 2y^2 = 0\).
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Answer: \(k = \frac{11}{2}\)
Every point of \(2x + y = 0\), i.e. \(y = -2x\), satisfies the given equation. Substituting:
\(3x^2 + kx(-2x) + 2(-2x)^2 = 0 \Rightarrow 3x^2 - 2kx^2 + 8x^2 = 0 \Rightarrow (11 - 2k)x^2 = 0\).
This holds for all \(x\), so \(11 - 2k = 0\) and \(k = \frac{11}{2}\).
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· 28 Oct 2026
AI-verified · Oct 2026
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