# Determining if subspace of P4

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• Apr 22nd 2008, 06:47 PM
pakman
Determining if subspace of P4
I have to prove that the set of all polynomials in P4 having at one real root is not a subspace of P4. However I don't know what they mean by having at least one real root. Any ideas?
• Apr 22nd 2008, 07:05 PM
ThePerfectHacker
The terms "at least one real root" means among the zeros of a polynomial one of the zeros is a real number. For example, $x^2+1$ has two zeros $i,-i$ both of them are not real. While $x^3+x$ has at least one real root, i.e. $0$.