Putting x=1, we see that the equation is satisfied. So 1 is a root of the equation. This is verification.
In fact, you can find the conditions when 1 will be a root of the general quadratic equation Ax2+Bx+C=0, by,
where the last equality comes from the fact that in a quadratic equation, A is non-zero.
So 1 is a root if and only if the sum of the coefficients is 0. (Again this can be verified by putting x=1 in the general equation directly.)