Task 304
Task 304: test task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. A cubic polynomial $f(x) = x^3 + ax^2 + bx + c$ with at least two distinct roots has the following properties: (i) The sum of all the roots is equal to twice the product of all the roots. (ii) The sum of the…
The task
A cubic polynomial $f(x) = x^3 + ax^2 + bx + c$ with at least two distinct roots has the following properties: (i) The sum of all the roots is equal to twice the product of all the roots. (ii) The sum of the squares of all the roots is equal to 3 times the product of all the roots. (iii) $f(1) = 1.$ Find $c.$