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Qu: Let a1,a2.........an be greater than or equal to zero. P(x)= xn+a1xn-1+.........+an-1x+1 has n real roots. find least value of P(2).options: a)3n b)2n c) 1 d) none

sanpreet gill , 15 Years ago

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1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello Student,
Please find answer to your question below

$P(x) = x^n + a_{1}x^{n-1} + a_{2}x^{n-2} + a_{3}x^{n-3} + ..........+a_{n-1}x + a_{n}$

Since a₁, a₂, a₃…......a_nall are greater than or equal to zero.
$P(2) = 2^n + a_{1}2^{n-1} + a_{2}2^{n-2} + a_{3}2^{n-3} + ..........+a_{n-1}2 + a_{n}$
Since all the coefficients are greater than or equal to zero. No coeffiecient is negative.
So minimum of P(2) will be at when all the coefficients are zero.
$[P(2)]_{min} = 2^n$

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