{"status": "success", "data": {"description_md": "*This is a user suggested problem. The TopsOJ staff thanks and gives full credit to [ Maximilian113](https://www.topsoj.com/users/Maximilian113/profile) for their contribution.*\n\n****\n\nLet $q(x)$ be a monic quadratic. Suppose $q(x)$ has roots $r_1, r_2$ satisfying the following properties:\n\n**1.** $r_1 =\\frac{1}{r_2}$\n**2.** $r_1, r_2$ are of the form $a \\pm b \\sqrt{c},$ where $a, b, c$ are positive integers, $c$ is not divisible by the square of any prime, and $a = b + c.$\n\nFind the sum of all possible values of $q(-2)$.", "description_html": "

This is a user suggested problem. The TopsOJ staff thanks and gives full credit to Maximilian113 for their contribution.

Let q(x) be a monic quadratic. Suppose q(x) has roots r_1, r_2 satisfying the following properties:

1. r_1 =\\frac{1}{r_2}
2. r_1, r_2 are of the form a \\pm b \\sqrt{c}, where a, b, c are positive integers, c is not divisible by the square of any prime, and a = b + c.

Find the sum of all possible values of q(-2).

", "hints_md": "If you have a discriminant, try bounding.", "hints_html": "

If you have a discriminant, try bounding.

", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "M2: Reciprocal Roots", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}