What is a third-degree polynomial function P(x) with rational coefficients so that P(x) = 0 has roots −3 and i?

x²-(i-3)x- 3i

Step-by-step explanation:

What is a third-degree polynomial function P(x) with rational coefficients so that P(x) = 0 has roots −3 and i?

Given the toots of the polynomial to be -3 and i, the factors of the polynomial will be (x+3) and (x-i)

Taking the product

P(x) = (x+3)(x-i)

P(x) = x²-xi+3x-3i

P(x) = x²-(i-3)x- 3i

Hence the required polynomial is

x²-(i-3)x- 3i

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step-by-step explanation:

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