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Question

If α,β be unequal real roots of the equation ax2+bx+c=0 where a,b,c are real and γ is the solution of 2ax+b=0 then

A
γ>α,γ>β
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B
γ>α,γ<β
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C
α<γ<β or β<γ<α
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D
none of these
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Solution

The correct option is A α<γ<β or β<γ<α
α & β are the roots of the equation f(x)=ax2+bx+c=0
for α>β
Since, roots are real
There lies a γ such that f(γ)=0 for β<γ<α
2aγ+b=0
Similarly for α<β, we get α<γ<β
Ans: C

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