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

Ans:Hello Student,Please find answer to your question belowSince a1, a2, a3…......anall are greater than or equal to zero.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.

BACK

Algebra> theory of equations...

Qu: Let a₁,a₂.........a_n be greater than or equal to zero. P(x)= xⁿ+a₁x^n-1+.........+a_n-1x+1 has n real roots. find least value of P(2).

options: a)3n b)2n c) 1 d) none

sanpreet gill , 16 Years ago

Grade

1 Answers

Jitender Singh

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.
$[P(2)]_{min} = 2^n$