2014-philic Cubic

Algebra Level 5

Let P(x)=x3(2014+22014)x+4028P(x)=x^3-(2014+2\sqrt{2014})x+4028

If the smallest root of P(x)P(x) is r1r_1, and the other two roots are r2r_2 and r3r_3, then r2×r3r_2\times r_3 can be expressed as a+b+cda+\sqrt{b+c\sqrt{d}} for integers a,b,c,da, b, c, d with dd square-free. Find a+b+c+d(mod10000)a+b+c+d\pmod{10000}

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

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