CAT (QA) PYQs

The equation $x^3 + (2r + 1)x^2 + (4r - 1)x + 2 = 0$ has $- 2$ as one of the roots. If the other two roots are real, then the minimum possible non-negative integer value of $r$ is

If $f(x)=(x^2+3x)(x^2+3x+2)$, then the sum of all real roots of the equation $\sqrt{f(x)+1}=9701$, is

Let $m$ and $n$ be positive integers, If $x^2 + mx + 2n = 0$ and $x^2 + 2nx + m = 0$ have real roots, then the smallest possible value of $m + n$ is