# Does a polynomial of degree n necessarily have n real solutions? Does it necessarily have n unique solutions, real or imaginary?

No. A polynomial equation in one variable of degree $n$ has exactly $n$ Complex roots, some of which may be Real, but some may be repeated roots.
For example, $0 = {x}^{4} + 2 {x}^{2} + 1 = {\left(x - i\right)}^{2} {\left(x + i\right)}^{2}$ has roots $i$, $i$, $- i$, $- i$.
If the polynomial has Real coefficients, then any Complex roots occur as conjugate pairs. So if a polynomial of degree $n$ has Real coefficients, then it has $n - 2 k$ Real roots and $2 k$ non-Real Complex roots for some integer $k \ge 0$ counting repeated roots.