IPMAT Indore (MCQ) PYQs

The number of values $a$ can take such that $x^4 + ax^3 + (3a - 4)x^2 + 2(a - 1)x - 4$ can be expressed as a product of two quadratic polynomials, $x^2 + px + 2$ and $x^2 + qx - 2$, where $p$ and $q$ are real, is

The number of real solutions of the equation $(x^2 - 15x + 55)^{x^2-5x+6} = 1$ is:

Let $f(x) = a^2x^2 + 2bx + c$ where, $a \neq 0$, $b, c$ are real numbers and $x$ is a real variable then