Find the zeros of the following quadratic polynomial: $5x^2 + 8x + 3$.

Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively: $\frac{1}{4}, -1$.

Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial: $4x^{2} + 5\sqrt{2}x - 3$

State the degree of the following polynomial: $p(x) = (x^{1/2})^{50} - 5x^{10} - 9x^2 + 15$.

The product of the zeros of the polynomial $kx^{3}-6x^{2}+11x-6$ is $4$. Find the value of $k$.

If $p(x) = x^{3} - 3x^{2} - x + 3$ is divided by $x - 1$,then the remainder is .............