# How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are 3-i, 5i?

##### 1 Answer
Nov 27, 2016

${x}^{4} - 6 {x}^{3} + 35 {x}^{2} - 150 x + 250$.

#### Explanation:

Complex roots occur in conjugate pairs. The zeros of the required

polynomial are $\pm 5 i \mathmr{and} 3 \pm i$m and so it is

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

$= \left({x}^{2} + 25\right) \left({\left(x - 3\right)}^{2} + 1\right)$

$= \left({x}^{2} + 25\right) \left({x}^{2} - 6 x + 10\right)$

$= {x}^{4} - 6 {x}^{3} + 35 {x}^{2} - 150 x + 250$.

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