Choosing a constant value so that one of the roots is 2

Question

Take a look at this polynomial $$ x^3 - x^2 -2x + a = 0 $$ Is it possible to choose a constant value for $a$ so that one of the roots is 2 other than choosing $a$ to be zero? If not, is there any proof shows that it is impossible to have a root of 2 if $a\neq 0$?

Answer 1

If $2$ is a root then we need: $$2^3-2^2-2\cdot2+a=0,$$ otherwise $2$ is not a root of the equation.

Answer 2

For there to be a root at $x = 2$, $$2^3-2^2-2*2+a=0$$ must be satisfied. Simplifying this finds $$a=0$$ must be satisfied. Therefore $a = 0$ is the only way $x = 2$ will be a root.