Polynomial Root and Evaluation

Suppose you have a polynomial expressed as:

$$P(x) = 2x^3 - 3x^2 + ax - 5$$

where $$a$$ is a constant. It is given that the polynomial has a root at $$x = 2$$. Determine the value of $$a$$ such that this condition holds. After finding the value of $$a$$, compute $$P(1)$$.