Coefficients of Polynomial add to 0 iff 1 is a Root

Theorem
Let $\map E x$ be the equation in $x$ represented as:


 * $\ds \sum_{j \mathop = 0}^n a_j x^j = 0$

where the $a_j$s are constants.

Then $x$ is a root of $\map E x$ :
 * $\ds \sum_{j \mathop = 0}^n a_j = 0$

That is, $x$ is a root of $\map E x$ all the coefficients of the polynomial in $x$ sum to zero.

Proof
Letting $x = 1$ in $E$;