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Question
If 2x + y = 0 is one of the lines represented by 3x2 + kxy + 2y2 = 0, then the value of k is
Options
`1/2`
`11/2`
`5/2`
`(-11)/2`
Solution
Auxiliary equation of the given equation is 2m2 + km + 3 = 0.
Slope of the line 2x + y = 0 is m = − 2.
∴ m = −2 is a root of the auxiliary equation 2m2 + km + 3 = 0
∴ 2(−2)2 − 2k + 3 = 0
∴ 8 − 2k + 3 = 0
∴ k = `11/2`
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