How do you write a polynomial function in standard form with real coefficients whose zeros include 3, 5i, and -5i?

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How do you write a polynomial function in standard form with real coefficients whose zeros include 3, 5i, and -5i?

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Answer 1 · 2016-05-07T13:50:15

The polynomial function in standard form with real coefficients whose zeros include $3$ $3$ , $5 i$ $5i$ , and $- 5 i$ $-5i$ is $x^{3} - 3 x^{2} + 25 x - 75$ $x^3-3x^2+25x-75$

Explanation:

A polynomial function with zeros as $a$ $a$ , $b$ $b$ and $c$ $c$ would be

$(x - a) (x - b) (x - c)$ $(x-a)(x-b)(x-c)$

Hence a polynomial function with zeros as $3$ $3$ , $5 i$ $5i$ and $- 5 i$ $-5i$ would be

$(x - 3) (x - 5 i) (x - (- 5 i))$ $(x-3)(x-5i)(x-(-5i))$ or

$(x - 3) (x - 5 i) (x + 5 i)$ $(x-3)(x-5i)(x+5i)$ or

$(x - 3) (x^{2} - {(5 i)}^{2})$ $(x-3)(x^2-(5i)^2)$ or

$(x - 3) (x^{2} - 25 i^{2})$ $(x-3)(x^2-25i^2)$ or

$(x - 3) (x^{2} + 25)$ $(x-3)(x^2+25)$ or

$x^{3} - 3 x^{2} + 25 x - 75$ $x^3-3x^2+25x-75$

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How do you write a polynomial function in standard form with real coefficients whose zeros include 3, 5i, and -5i?

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