How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are 3i, -3i, 5?

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Answer 1 · 2016-10-03T07:00:12

$y = (x -5)(x - 3i)(x - -3i) = x³ - 5x² + 9x - 45$

With any polynomial the with roots $r_1, r_2, r_3, ... r_n$ , the factors are:

$y = k(x - r_1)(x - r_2)(x - r_3)...(x - r_n)$

In this case, we are given that k = 1, and the roots are $5, 3i, and -3i$ . This makes the factors:

$y = (x -5)(x - 3i)(x - -3i)$

I will multiply the factors one-pair-at-a-time:

$y = (x - 5)(x² + 9)$

$y = x³ - 5x² + 9x + 45$