(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given the function "P" defined by: P(x) := x^2n + a2n-1*x^2n-1 + ... + a1x + a0;

prove that there exists an x* in |R such that P(x*) = inf{P(x) : x belongs to | R}

Also, prove that:

|P(x*)| = inf{|P(x)| : x belongs to |R}

3. The attempt at a solution

As the function is the sum of continuous functions, it is contnuos too.

Then, I thought about the theorem according to which if we have a cont. function on a sequentially compact space, it has inf. and sup. therein.

But the space here is not sequentially compact.

Can I use this theorem all the same, by adding some restrictions, perhaps?

thanksss

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Polynomial function: infimum

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