CAT (QA) PYQs

The number of distinct real roots of the equation $(x + \frac{1}{x})^2 - 3(x + \frac{1}{x}) + 2 = 0$ equals

Let $a, b, c$ be non-zero real numbers such that $b^2 < 4ac$, and $f(x) = ax^2 + bx + c$. If the set S consists of all integers m such that $f(m) < 0$, then the set S must necessarily be

Let $r$ and $c$ be real numbers, if $r$ and $-r$ are roots of $5 x^{3}+c x^{2}-10 x+9=0$, then $c$ equals