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This essential trains for: SAT-II, AMC-10, AMC-12, AIME, Math Kangaroo 9-10.

The coefficients and the roots of polynomial equations with __complex coefficients__ are related. The equations describing how they relate are called Viète's relations.

For a polynomial equation of degree n:

with roots:

the canonical expression and the factored expression must be identical:

Using the definition of equal polynomials:

Note that the system of equations with unknowns

However, the relations may be very useful in answering auxiliary questions about the equation.