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Find k, if one of the lines given by 6x2 + kxy + y2 = 0 is 2x + y = 0. |
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Answer» Given equation is 6x2 + kxy + y2 = 0. Its auxiliary equation is m2 + km + 6 = 0 Since, 2x + y = 0 is one of the lines given by 6x2 + kxy + y2 = 0 Slope of the line 2x + y = 0 is -2. ∴ - 2 is one of the roots of the auxiliary equation m2 + km + 6 = 0 ∴ (- 2)2 + k(-2) + 6 = 0 ∴ 4 - 2k + 6 = 0 ∴ 2k = 10 ∴ k = 5 |
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