Proving Quadratic Basis for P(2): t2+2t+1, t2+t, t2+1

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Prove that t2+2t+1,t2+t, t2+1 is a basis for the space of quadratic polynomials P(2).
 
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mandygirl22 said:
Prove that t2+2t+1,t2+t, t2+1 is a basis for the space of quadratic polynomials P(2).
How do you show that the elements in a set are a basis for a vector space (which includes your function space)?
 

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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