IIM-K (BMSAT) 2025 (QA) PYQs

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?

If $8x^2 - 2kx + k = 0$ is a quadratic equation in $x$, such that one of its roots is $p$ times the other, and $p, k$ are positive real numbers, then $k$ equals

If one of the roots of the equation $x^2 + ax + 3a = 0$ is $1$, then its other root is