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How do you write a polynomial in standard form given the zeros 5 and 1+2i?

1 Answer

Mar 26, 2018

$x^{3} - 7 x^{2} + 15 x - 25$ $x^3-7x^2+15x-25$

Explanation:

If $1 + 2 i$ $1+2i$ is root of a polynomial, $1 - 2 i$ $1-2i$ also the root of it. Hence,

$P (x) = (x - 5) (x - 1 + 2 i) (x - 1 - 2 i)$ $P(x)=(x-5)(x-1+2i)(x-1-2i)$

= $(x - 5) (x^{2} - 2 x + 5)$ $(x-5)(x^2-2x+5)$

= $x^{3} - 7 x^{2} + 15 x - 25$ $x^3-7x^2+15x-25$

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