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

If $\alpha, \beta$ and $\gamma$ are the zeros of the cubic polynomial $p(x) = x^{3} - 6x^{2} - 7x$,then $\alpha + \beta + \gamma = \ldots$

Obtain the sum and the product of the zeros of the quadratic polynomial $6x^{2} - 7x - 3$ without finding the zeros.

The total cost of $(x+1)$ cameras is ₹ $(x^{3}+3x^{2}+5x+3)$. Find the cost of one camera.

Draw the graph of $p(x) = 3 - 2x - x^2$ and find the zeros of this polynomial.

Prove that $-6, -\frac{1}{2}$ and $1$ are the zeros of the cubic polynomial $p(x) = 2x^3 + 11x^2 - 7x - 6$. Also,verify the relationship between the zeros and the coefficients.