Find a cubic polynomial given zeros and leading coefficient

Firstly, we can ignore the leading coefficient of 1, as 1 is always assumed to be the leading coefficient in the absence of another leading coefficient. Next, we now that every imaginary zero has to have a negative counterpart. Therefore, our zeros are 2, 3i, and -3i. Next, we put these zeros into factored form. This gives us f(x) = (x - 2)(x - 3i)(x + 3i). Now, all we have to do is multiply out and combine all like terms. This gives us an answer of f(x) = x^3 - 2x^2 + 9x - 18.

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the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.