List of top Mathematics Questions on Polynomials asked in IPU CET

Given that \( \alpha_1, \alpha_2, \alpha_3 \) are the roots of \( 3x^3 - x^2 - 10x + 8 = 0 \), then the value of \( \alpha_1^2 + \alpha_2^2 + \alpha_3^2 \) is

Choose the most appropriate options.
Let \( f(x) = ax^3 + 5x^2 - bx + 1 \). If when divided by \( x - 1 \) it leaves a remainder of 5, and \( f(x) \) is divisible by \( 3x - 1 \), then

If \(P(x)\) is a polynomial such that \[ P(x^2 + 1) = \{P(x)\}^2 + 1 \] then \(P'(0)\) is equal to