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Hi,

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

I was wondering whether I could prove the following using induction? I have tried, and was successful, am simply now not sure whether employing induction in this case is just.

I am asked to show that for any odd-power polynomial P_{2n-1}, there exists a number a, real, so that P_{2n-1}(a)=0.

I first thought of using continuity, but wasn't sure how to proceed in that direction so managed to show it via induction. Is it valid?

2. Relevant equations

3. The attempt at a solution

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# Homework Help: P 2n-1 (a)=0 for some a, real.

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