The product of the zeros of a quadratic polynomial $p(x) = 3x^2 + 7x + 4$ is..........

Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial:
$v^{2}+4 \sqrt{3} v-15$

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

For which values of $a$ and $b$ are the zeroes of $q(x) = x^{3} + 2x^{2} + a$ also the zeroes of the polynomial $p(x) = x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x + b$? Which zeroes of $p(x)$ are not the zeroes of $q(x)$?

Obtain a quadratic polynomial with the following conditions:
The sum of the zeros $= \frac{1}{4}$;
The product of the zeros $= -1$.

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.