Let r1,r2,r3 be the roots of polynomial P(x)=x3+3x+1. Evaluate the product k=1∏3(rk2+rk+1).
This problem is posed by Francisco R.
Details and assumptions
For those unfamiliar with the product notation,
k=1∏3(rk2+rk+1)=(r12+r1+1)(r22+r2+1)(r32+r3+1).