The polynomial $3{x^3} + 2{x^2} + \alpha x + b$, where $\alpha $ and $b$ are constants, is denoted by $p\left( x \right)$. It is given that $\left( {x - 1} \right)$ is a factor of $p\left( x \right)$, and that when $p\left( x \right)$ is divided by $\left( {x - 2} \right)$ the remainder is 10.
a) Find the values of $\alpha $ and $b$.
b) When $\alpha $ and $b$ have these values, solve the equation $p\left( x \right) = 0$.
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