MCQ

If 2x + y = 0 is one of the lines represented by 3x^{2} + kxy + 2y^{2} = 0, then the value of k is

#### Options

`1/2`

`11/2`

`5/2`

`(-11)/2`

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#### Solution

Auxiliary equation of the given equation is 2m^{2} + km + 3 = 0.

Slope of the line 2x + y = 0 is m = − 2.

∴ m = −2 is a root of the auxiliary equation 2m^{2} + km + 3 = 0

∴ 2(−2)^{2} − 2k + 3 = 0

∴ 8 − 2k + 3 = 0

∴ k = `11/2`

Concept: Pair of Straight Lines - Pair of Lines Passing Through Origin - Combined Equation

Is there an error in this question or solution?

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