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Question

If a, b, c are in H.P., and α, β are the roots of the equation bcx2+ 2cax+ ab = 0, then the value of α + β + αβ is-

A
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B
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C
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D
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Solution

The correct option is A 0
a,b,c are in H.P
2b=1a+1c
b=2aca+c
Let α and β be the roots of bcx2+2cax+ab=0
α+β=2cabc=2ab
αβ=abbc=ac
α+β+αβ=2ab+ac
=2ac+abbc
=2ab+ac
=2a2aca+c+ac where b=2aca+c
=2a(a+c)2ac+ac
=acc+ac
=ac1+ac=1

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