IIM-B (BBA-DBE) 2024 #2 (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

If the minimum value of $f(x) = x^2 + 2bx + 2c^2$ is greater than the maximum value of $g(x) = -x^2 - 2cx + b^2$, then for real value of x.

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