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Find a degree 3 polynomial with real coefficients having zeros 3 and 3−3i and a lead coefficient of 1. Write P in expanded form.

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MathPhys

Answer:

P =  x³ − 9x² + 36x − 54

Step-by-step explanation:

Complex roots come in conjugate pairs.  So if 3−3i is a zero, then 3+3i is also a zero.

P = (x − 3) (x − (3−3i)) (x − (3+3i))

P = (x − 3) (x − 3 + 3i) (x − 3 − 3i)

P = (x − 3) ((x − 3)² − (3i)²)

P = (x − 3) ((x − 3)² + 9)

P =  (x − 3)³ + 9 (x − 3)

P =  x³ − 9x² + 27x − 27 + 9x − 27

P =  x³ − 9x² + 36x − 54

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