If $\alpha$ and $\beta$ are the zeros of the polynomial $P(x) = x^2 - 3x + 2k$ and $\alpha + \beta = \alpha\beta$,then the value of $k$ 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:
$7 y^{2}-\frac{11}{3} y-\frac{2}{3}$

The number of the zeros of $p(x) = x^{2} - 9$ is............

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

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

If $x+1$ is a factor of $2x^{3}+ax^{2}+2bx+1$,then find the values of $a$ and $b$ given that $2a-3b=4$.