CAT (QA) PYQs

If the equations $x^2 + mx + 9 = 0$, $x^2 + nx + 17 = 0$, and $x^2 + (m + n)x + 35 = 0$ have a common negative root, then the value of $2m + 3n$ is

If $x$ and $y$ are real numbers such that $4x^2 + 4y^2 - 4xy - 6y + 3 = 0$, then the value of $(4x + 5y)$ is

Let $f(x)=x^{2}+a x+b$ and $g(x)=f(x+1)-f(x-1)$. If $f(x) \geq 0$ for all real $x$, and $g(20)=72$, then the smallest possible value of $b$ is