If the equation \[{{a}_{n}}{{x}^{n}}+{{a}_{n-1}}{{x}^{n-1}}+....+{{a}_{1}}x=0\], \[{{a}_{1}}\ne 0\], \[\,n\ge 2\], has a positive root \[x=\alpha \], then the equation \[n{{a}_{n}}{{x}^{n-1}}+(n-1){{a}_{n-1}}{{x}^{n-2}}+....+{{a}_{1}}=0\] has a positive root, which is [AIEEE 2005]

If the equation \[{{a}_{n}}{{x}^{n}}+{{a}_{n-1}}{{x}^{n-1}}+....+{{a}_

1.	If the equation \[{{a}_{n}}{{x}^{n}}+{{a}_{n-1}}{{x}^{n-1}}+....+{{a}_{1}}x=0\], \[{{a}_{1}}\ne 0\], \[\,n\ge 2\], has a positive root \[x=\alpha \], then the equation \[n{{a}_{n}}{{x}^{n-1}}+(n-1){{a}_{n-1}}{{x}^{n-2}}+....+{{a}_{1}}=0\] has a positive root, which is [AIEEE 2005]
A.	Greater than or equal to a
B.	Equal to \[\alpha \]
C.	Greater than \[\alpha \]
D.	Smaller than \[\alpha \]
Answer» E.

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If the equation \[{{a}_{n}}{{x}^{n}}+{{a}_{n-1}}{{x}^{n-1}}+....+{{a}_{1}}x=0\], \[{{a}_{1}}\ne 0\], \[\,n\ge 2\], has a positive root \[x=\alpha \], then the equation \[n{{a}_{n}}{{x}^{n-1}}+(n-1){{a}_{n-1}}{{x}^{n-2}}+....+{{a}_{1}}=0\] has a positive root, which is [AIEEE 2005]

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