Problem #PRU-61022

Problems Calculus Derivative Derivative and multiple roots Algebra and arithmetic Polynomials Division of polynomials with remainders. The greatest common divisor (GCD) and the least common multiple (LCM) for polynomilas.

Problem

For which $A$ and $B$ does the polynomial $A x^{n + 1} + B x^{n} + 1$ have the number $x = 1$ at least two times as its root?

To see the solution register and get verified.