*changes name to Liam for a minute*
It very much depends on the polynomial and how you write it.
Suppose, for example, that you have the polynomial x3+x2+x+1 on its own. That has no solutions because it's not an equation. You could anyway work out the zeroes of that polynomial by letting it be equal to zero and solving x3+x2+x+1=0 . Then you'd get x3+x2+x+1 = (x+1)(x2+1) and you can't simplify it further.
On the other hand we've just found a polynomial that has no solutions, which was x2+1 = 0. Try any real number you can think of and you won't find one that satisfies this equation.
So not all polynomials have a solution when you're setting that polynomial equal to zero.
Of course, a few people would soon point out that in fact x2+1 =0 does have a solution, which is (x+i)(x-i), but I'm assuming that you've not learned about i and that you don't need to know yet. If, however, you're interested, i is the imaginary number that among other things allows all polynomials to have solutions. Its value is given by:
i2= -1.
That is, by definition it is the number that satisfies x2+1=0.
