ALGEBRA

Find a degree 3 polynomial with real coefficients having zeros
2 and 4-3i and a lead coefficient of 1.

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  1. if the coefficients are real, then the complex roots occur in pairs. So, our polynomial is

    (x-2)(x-(4-3i))(x-(4+3i))
    (x-2)((x-4)+3i)((x-4)-3i)
    (x-2)((x-4)^2+3^2)
    ...

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