IPMAT Indore 2024 (SA) PYQs

If the harmonic mean of the roots of the equation $(5 + \sqrt{2}) x ^ 2 - bx + 8 + 2\sqrt{5} = 0$ is $4$ then the value of $b$ is

The difference between the maximum real root and the minimum real root of the equation $(x^2 - 5)^4 + (x^2 - 7)^4 = 16$ is

If $a_1, a_2, ..., a_8$ are the roots of the equation $x^8 + x^7 + ... + x + 1 = 0$, then the value of $a_1^{2025} + a_2^{2025} + ... + a_8^{2025}$ is