The graph of linear polynomial $p(x) = 3x - 6$ intersects the $X$-axis at $\ldots......$

Obtain the sum and the product of the zeros of the following quadratic polynomial without finding the zeros: $4x^{2} - 4x + 1$.

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 $q(x)$?

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

From the following figure,find the number of real zeros of $y=p(x)$ :

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