Problem #PRU-78003

Problems Algebra and arithmetic Number theory. Divisibility Arithmetic functions Polynomials Polynomials(other)

Problem

Prove that if $x_{0}^{4} + a_{1} x_{0}^{3} + a_{2} x_{0}^{2} + a_{3} x_{0} + a_{4}$ and $4 x_{0}^{3} + 3 a_{1} x_{0}^{2} + 2 a_{2} x_{0} + a_{3} = 0$ then $x^{4} + a_{1} x^{3} + a_{2} x^{2} + a_{3} x + a_{4}$ is divisible by $(x - x_{0})^{2}$ .

To see the solution register and get verified.