If the roots of the equation $x^{2}-p x+54=0$ are in the ratio $2: 3$, then value of $p$ is:

Amit and Alok attempted to solve a quadratic equation. Amit made a mistake in writing down the constant term and ended up with roots $(4, 3)$. Alok made a mistake in writing down coefficient of $x$ to get roots $(3, 2)$. The correct roots of the equation are:

If one root of the quadratic equation $ax^2+bx+c=0$ is the reciprocal of other, then which of the following is correct?

If $\alpha$ and $\beta$ are the roots of the equation $a x^{2}+b x+c=0$, then value of

$\frac{1}{a \alpha+b}+\frac{1}{a \beta+b}$ is :

If $\sin (\alpha)$ and $\cos (\alpha)$ are the roots of the equation $a x^{2}+b x+c=0$, then $b^{2}$ is

The graph of a polynomial $y = f(x)$ is shown in figure below, then the number of its zeros is:

Match List I with List II. Choose the correct answer from the options given below: