CGMO 2020 Problem 5

Find all the real number sequences $\{b_n\}_{n \geq 1}$ and $\{c_n\}_{n \geq 1}$ that satisfy the following conditions: (i) For any positive integer $n$ , $b_n \leq c_n$ ; (ii) For any positive integer $n$ , $b_{n+1}$ and $c_{n+1}$ is the two roots of the equation $x^2+b_nx+c_n=0$ .