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Question

If the roots of the equation x3lx2+mxn=0 are in H.P., then the mean root is

A
3nm
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B
2nm
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C
nm
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D
nm
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Solution

The correct option is B 3nm
As roots are in H.P the let α,β,γ roots of x3lx2+mxn=0
S1=α+β+γ=lS2=αβ+βγ+γα=mS3=αβγ=n
Now as α,β,γ are in H.P
Then 1α,1β,1γ are in A.P
Hence,
Mean of A.P is αβ+βγ+γα3αβγ
So mean of H.P is 3αβγαβ+βγ+γα=3nm

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