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#### PurpleDude

##### New member

- Feb 7, 2014

- 10

Hello everyone!

I have this polynomial: $p(x) =$ \(\displaystyle 1 + \sum_{k=1}^{13}\frac{(-1)^k}{k^2}x^k\)

- I'm supposed to show that this polynomial must have at least one positive real root.

- I'm supposed to show that this polynomial has no negative real roots.

- And I'm supposed to show that if $z$ is any root of this polynomial, then $|z| < 170$

I do not know how to start this question, so any guidance on these three steps would be appreciated.

I have this polynomial: $p(x) =$ \(\displaystyle 1 + \sum_{k=1}^{13}\frac{(-1)^k}{k^2}x^k\)

- I'm supposed to show that this polynomial must have at least one positive real root.

- I'm supposed to show that this polynomial has no negative real roots.

- And I'm supposed to show that if $z$ is any root of this polynomial, then $|z| < 170$

I do not know how to start this question, so any guidance on these three steps would be appreciated.

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