JIPMAT (QA) PYQs

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:

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: