IIM-K (BMSAT) 2025 (QA) PYQs

If the harmonic mean of the roots of the equation $(5 + \sqrt{2}) x ^ 2 - bx + 8 + 2\sqrt{5} = 0$ is $4$ then the value of $b$ is

The zeroes of $ax² + bx + c = 0$ are in the ratio $1:2$ (assume the coefficients to be non-zero). Which of these is one of the zeroes?

Let $f(x) = a^2x^2 + 2bx + c$ where, $a \neq 0$, $b, c$ are real numbers and $x$ is a real variable then