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If the equation a(n)x^(n)+a(n-1)x^(n-1)+...

If the equation `a_(n)x^(n)+a_(n-1)x^(n-1)+..+a_(1)x=0, a_(1)!=0, n ge2`, has a positive root `x=alpha` then the equation `na_(n)x^(n-1)+(n-1)a_(n-1)x^(n-2)+….+a_(1)=0` has a positive root which is

A

greater than or equal to `alpha`

B

equal to `alpha`

C

greater than `alpha`

D

smaller than `alpha`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `f(x)=a_(n)x^(n)+a_(n-1)x^(n-1)+……….+a_(1)x`
`f(0)=0,f(alpha)=0`
`f'(x)=0` has atleast one root between `(0,alpha)`
i.e. Equation
`na_(n)x^(n-1)+(n-1)a_(n-1)x^(n-2)+….+a_(1)=0`
has a positive root smaller than `alpha`.
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