BMSAT Kozhikode (QA) PYQs

What is the condition for $x^2 + (a + b)x + ab$, with a and b non-zero, to have real roots?

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

What must be added to $x^4+2x^3-2x^2+x-1$ so that the result is exactly divisible by $x^2+2x-3$?