What roots are you talking about?

Because the answer is a degree of a polynomial and it is an integer, the answer is a nonnegative integer (0, 1, 2, ...). (The polynomial $x \mapsto 0$ has degree $-\infty$ .)

Now, if the answer is 0, then the polynomial is constant: $x \mapsto c$ where $c \neq 0$ . But this polynomial has no root at all, so 0 cannot be a root of this polynomial.

An answer of 1 works, with the polynomial $x \mapsto x-1$ , having degree 1 and that 1 is a solution. Thus the answer is 1 .

It's answer is 1 because in the question it is given that degree of the polynomial is least and has a root whose value is an integer. 1 is that smallest number.