# Newtons polynomial

Algebra Level 5

The polynomial $$x^3+Mx-N$$ has roots $$a,b$$ and $$c$$, where $$M$$ and $$N$$ are constant integers satisfying the inequality $$1<|M| <|N|$$.

Given that $$a^5 +b^5+c^5=90$$ and $$a^6 + b^6 + c^6 = 227$$, find the value of $$M^5 + N^5$$.

×