How do you write the simplest polynomial function with the zeros 2i, -2i and 6?

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How do you write the simplest polynomial function with the zeros 2i, -2i and 6?

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Answer 1 · 2016-11-14T16:56:38

Please see the explanation.

Explanation:

The factor that corresponds to the zero, $2i$ , is $(x - 2i)$ .
The factor that corresponds to the zero, $-2i$ , is $(x + 2i)$ .
The factor that corresponds to the zero, $6$ , is $(x - 6)$ .

Collect the factors into an equation:

$y = (x - 2i)(x + 2i)(x - 6)$

We can use the pattern, $(a - b)(a + b) = a^2 - b^2$ , to multiply the first two factors:

$y = (x^2 - 4i^2)(x - 6)$

Use the property $i^2 = -1$ to simplify the first factor:

$y = (x^2 + 4)(x - 6)$

Use the F.O.I.L. method to multiply the remaining factors:

$y = x^3 - 6x^2 + 4x - 24$

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How do you write the simplest polynomial function with the zeros 2i, -2i and 6?

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