# 2014-philic Cubic

Algebra Level 5

Let $P(x)=x^3-(2014+2\sqrt{2014})x+4028$

If the smallest root of $$P(x)$$ is $$r_1$$, and the other two roots are $$r_2$$ and $$r_3$$, then $$r_2\times r_3$$ can be expressed as $a+\sqrt{b+c\sqrt{d}}$ for integers $$a, b, c, d$$ with $$d$$ square-free. Find $a+b+c+d\pmod{10000}$

Note: if you are going to use Wolfram Alpha, don't even bother answering the problem (cheater!)

×