# A problem by Diego E. Nazario Ojeda

Level pending

A member of Brilliant remembers the previous system, in which members received $$4$$ weekly problems of each topic, with $$3$$ opportunities for each problem. He remembers that one week, in Number Theory, he got all the problems correct, but he gave two wrong answers previously. This event is possible in $$x$$ ways. If $$-x$$ is the only root of a polynomial of degree $$2$$, what is the sum of the coefficients of that polynomial?

Details

The order of the answers doesn't matters. Getting a wrong answer in the second and third problem is the same if you answer first the second, or the third.

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