SOLUTION: The equation of a polynomial with real coefficients that has the roots 2 and 3(imaginary i) is? a. x^3-2x^2+9x-18 b. x^3-2x^2-12x-18 c. x^3+2x^2-9x-18 d. x^3-2x^2+9x-20

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Let's call the polynomial P(x). If 2 and 3i are roots of P(x) then P(x) must be:

If this isn't immediately clear, think about it. If 2 is a root of P(x) then, by the very definition of a root, when x = 2, P(x) = 0. Can you see that if x = 2 in the equation above, that P(x) = 0? And similarly, can you see that if x = 3i (or -3i) that P(x) is zero (because if x = 3i (or -3i)?

Now all we need to do is multiply out P(x) to see which answer is correct. we should get:
so (a) is correct.