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?
The terms "at least one real root" means among the zeros of a polynomial one of the zeros is a real number. For example, $\displaystyle x^2+1$ has two zeros $\displaystyle i,-i$ both of them are not real. While $\displaystyle x^3+x$ has at least one real root, i.e. $\displaystyle 0$.