If 2x2+7xy+3y2+8x+14y+λ=0 represents a pair of straight lines, then the value of λ is
A
4
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B
−3
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C
8
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D
6
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Solution
The correct option is C8 The equation ax2+2hxy+by2+2gx+2fy+c=0
represents a pair of straight lines, if abc+2fgh−af2−bg2−ch2=0.
Hence, 2x2+7xy+3y2+8x+14y+λ=0 represents a pair of straight lines if 6λ+2(7)(4)(72)−2(7)2−3(4)2−λ(72)2=0 ⇒6λ+196−98−48−49λ4=0 ⇒49λ4−6λ=196−146 ⇒25λ4=50 ⇒λ=50×425=8