CAT (QA) PYQs

Let $\alpha$ and $\beta$ be the two distinct roots of the equation $2x^2 - 6x + k = 0$, such that $(\alpha + \beta)$ and $\alpha\beta$ are the distinct roots of the equation $x^2 + px + p = 0$. Then, the value of $8 (k - p)$ is

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

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