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

Regarding the function $f(x)=x^{2}-5 x+1$ and $g(x)=1-x-x^{3}$ on the set of real numbers, which of the following statements is not true?

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