Find a cubic equation with integral coefficients that has 1 and 3 - i as roots. (Write your equation in the form ax^3 + bx^2 + cx + d = 0.)

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#1

Find a cubic equation with integral coefficients that has 1 and 3 - i as roots. (Write your equation in the form ax^3 + bx^2 + cx + d = 0.)

Answer:

complex roots occur in conjugate pairs … so 3 + i is also a root

if r is a root, then (x - r) is a factor

(x - 1)(x - 3 + i)(x - 3 - i) = 0

(x - 1)(x^2 - 6 x + 10) = 0