Find the number of real zeros of the following polynomial: $p(x) = x^{2} - 2x$.

If the zeros of the cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$ $(a \neq 0, a, b, c, d \in R)$ are $\alpha, \beta,$ and $\gamma$,then $\alpha\beta + \beta\gamma + \gamma\alpha = \dots$

Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial:
$y^{2}+\frac{3}{2} \sqrt{5} y-5$

If the sum of the zeros is $-3$ and the product of the zeros is $-4,$ then the quadratic polynomial is $\ldots \ldots \ldots$

Prove that $-2$,$4$,and $\frac{1}{2}$ are the zeros of the cubic polynomial $p(x) = 2x^3 - 5x^2 - 14x + 8$. Also,verify the relationship between the zeros and the coefficients.

The product of two polynomials is $3x^3 - x^2 - 3x + 1$ and one of the polynomials is $3x^2 + 2x - 1$. Find the other polynomial.