CAT (QA) PYQs

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

The quadratic equation $x² + bx + c = 0$ has two roots $4a$ and $3a,$ where a is an integer. Which of the following is a possible value of $b² + c$?

Let $A$ be a real number. Then the roots of the equation $x^2 - 4x - \log_2A = 0$ are real and distinct if and only if