Find a polynomial of lowest degree with rational coefficients that has the given numbers as some of its zeros? -4i, 5

Question

My teacher did a terrible job explaining and I was hoping I could get a better explanation of how to work these kinds of problems out.

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Answer 1 · 2018-02-25T17:21:14

$x^3-5x^2+16x-80$

$5, 4i, -4i$

So

$(x-4i)(x+4i)(x-5) " "$ Subtract all from $x$

$(x^2-4ix+4ix-16i^2)(x-5) " "$ FOIL the first two paratheses

$(x^2-16i^2)(x-5)" "$ Cancel the $4i$ terms

$(x^2+16)(x-5) " "i^2 =-1$ , so multiply $-16$ by $-1$

$x^3-5x^2+16x-80" "$ FOIL the remaining paratheses