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Consider the quartic polynomial \(P(x) = x^4 - 7x^3 + 14x^2 + 2x - 20\).
  1. It is given that \(z_1 = 3 + i\) is a root of the equation \(P(x) = 0\).
    1. Since \(P(x)\) has real coefficients, write down another complex root, \(z_2\).
    2. Find a real quadratic factor of \(P(x)\) corresponding to the roots \(z_1\) and \(z_2\).
  2. Hence, find the other two roots of the equation \(P(x) = 0\).
  3. Using the four roots of \(P(x)=0\), verify the sum of the roots using Vieta's formulas.

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