prove that $(p+p'+...+ p^{(n)}) \geq 0 $

Asked Jun 05 '15 at 14:22

Active Jun 05 '15 at 14:22

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Let $\forall x \in \mathbb R, \quad p(x) \geq 0$ where $p$ is a polynomial of order $n$ prove that ,

$$(p+p'+...+ p^{(n)}) \geq 0 \quad (\forall x \in \mathbb R) $$

explain : I tried induction on $n$ and taylor expansion to find a relation between coefficients .

asked Jun 05 '15 at 14:22

erfan soheil

Polynomial with real coefficients, yes? – MT_ Jun 05 '15 at 14:29
http://math.stackexchange.com/questions/599655/prove-that-for-a-polynomial-function-f-if-fx-geq-0-for-all-x-then-fx?rq=1 – Yimin Jun 05 '15 at 14:29
2

http://math.stackexchange.com/questions/397973/sum-of-polynoms-of-given-property – Yimin Jun 05 '15 at 14:30
in question did not mentioned this point but i think yes, the polynomial has real coefficients. – erfan soheil Jun 05 '15 at 14:31

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