I saw a mathematical problem where was given a wrong definition and was asked if some numbers satisfies the definition. Is this solution fine if there is a mistake in the definition?
A real number is algebraic if it is a root of some polynomial with integer coefficients. These polynomials are of the form $$P(x)=a_0+a_1x+a_2x^2+\cdots + a_nx^n$$ where the degree of the polynomial $n=1,2,3,\ldots$ and the coefficients $a_0,a_1,a_2,\ldots,a_n$ are integers.
Prove that the numbers $x=2/3$, $x=\sqrt 3$, $x=2+\sqrt{3}$, and $x=\sqrt{2}+\sqrt{3}$ are algebraic.
My solution is just to take $P(x)=0$.
Now the problem seems to be that zero polynomial satisfies the first sentence of the definition but not the second one. So what should a student answer as the first sentence of the definition and its explanation does not corresponds to each others?
This question was from the Finnish matriculation examination on autumn 2016.