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Difficulty Level:

Hard

MCQ

Suppose that P(z),Q(z)P(z), Q(z), and R(z)R(z) are polynomials with real coefficients, having degrees 2,3,2,3 , and 66 respectively, and constant terms 1,2,1,2 , and 33 , respectively.
Let NN be the number of distinct complex numbers zz that satisfy the equation P(z)Q(z)=R(z)P(z) \cdot Q(z)=R(z). What is the minimum possible value of NN ?

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