Suppose P is a quintic polynomial with real coefficients with P(0)=2 and P(1)=3 such that |z|=1 whenever z is a complex number satisfying P(z)=0. What is the smallest possible value of P(2) over all such polynomials P ?
Suppose P is a quintic polynomial with real coefficients with P(0)=2 and P(1)=3 such that |z|=1 whenever z is a complex number satisfying P(z)=0. What is the smallest possible value of P(2) over all such polynomials P ?