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How do you write the polynomial function given the following zeros: -3, -2i, 2i?

1 Answer

Oct 18, 2015

$f (x) = x^{3} + 3 x^{2} + 4 x + 12$ $f(x) = x^3+3x^2+4x+12$

Explanation:

$f (x) = (x + 3) (x + 2 i) (x - 2 i) = (x + 3) (x^{2} + 4)$ $f(x) = (x+3)(x+2i)(x-2i) = (x+3)(x^2+4)$

$= x^{3} + 3 x^{2} + 4 x + 12$ $= x^3+3x^2+4x+12$

Any polynomial in $x$ $x$ with these roots will be a multiple (scalar of polynomial) of this $f (x)$ $f(x)$ .

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