M and N: Relationship in Spanning and Subsets of Polynomials

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* If p1,p2,……pm span Pn, write down a mathematical relationship between m and n.

I know that Pn means the space of all polynomials of degree at most n, and this is an (n+1) dimension space, but I am not sure what kind of mathematical relationship the question is looking for :s

Any help is greatly appreciated!
 
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If Pn has dimension n+1, what must be true of any set that spans it? (In particular how many vectors are there in any basis?)
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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