A) 2
B) 6
C) 4
D) 1
Correct Answer: B
Solution :
We have, \[{{x}^{n}}-n{{x}^{n-1}}+{{a}_{2}}{{x}^{n-2}}+{{a}_{3}}{{x}^{n-3}}+...+\,{{a}_{n\,-\,1}}x+{{(-1)}^{n\,=\,0}}\] |
has ra positive roots. |
\[\therefore \]AM of all roots is equal to GM of roots, |
so all roots are equal and equal to 1. |
\[\therefore \]\[{{a}_{2}}={}^{n}{{C}_{2}}\]and \[{{a}_{3}}=-{}^{n}{{C}_{3}}\] |
\[\Rightarrow \]\[{{a}_{2}}+{{a}_{3}}={}^{n}{{C}_{2}}-{}^{n}{{C}_{3}}<0\] |
\[\Rightarrow \]\[n>2+3\] |
\[\Rightarrow \]\[n>5\] |
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