Find the number of real zeros of the following polynomial: $p(x) = 4x^2 + 11x + 10$.

Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial: $4x^2 - 3x - 1$

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.

If the zeros of the cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$ $(a \neq 0)$ are $\alpha, \beta,$ and $\gamma,$ then $\frac{1}{\alpha} + \frac{1}{\beta} + \frac{1}{\gamma} = \dots$

Obtain the quadratic or the cubic polynomial as the case may be in the standard form with the following coefficients: $a=6, b=-7, c=-3$.

If one zero of the quadratic polynomial $x^{2}+3x+k$ is $2$,then the value of $k$ is