If the zero of the polynomial $p(x) = 3x^{3} - x^{2} - ax - 45$ is $3$,then $a = \dots$

Given that the zeroes of the cubic polynomial $x^{3}-6x^{2}+3x+10$ are of the form $a, a+b, a+2b$ for some real numbers $a$ and $b$,find the values of $a$ and $b$ as well as the zeroes of the given polynomial.

The graph of $p(x) = x^{2} + 6x + 9$ intersects the $X$-axis $\ldots \ldots \ldots \ldots$

Find the zeros of the following quadratic polynomial: $p(x) = 3x^2 + 15x$. (in $, -5$)

If $\alpha, \beta$ and $\gamma$ are the zeros of the cubic polynomial $p(x) = x^{3} - 3x^{2} - 6x + 8$,then $\alpha \beta \gamma = \dots$

The zero of the linear polynomial $p(x) = ax + b$ is $\ldots \ldots \ldots \ldots$ $(a, b \neq 0)$.