BMSAT Kozhikode (QA) PYQs

Say for positive quantities a, b, $a + b$ equals $a^2 + ab + b^2$. Choose the nearest value to b if a is given as 0.5.

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

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