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

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Answer 1 · 2016-11-27T07:02:11

#x^4-6x^3+35x^2-150x+250#.

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

polynomial are #+-5i and 3+-i#m and so it is

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

#=(x^2+25)((x-3)^2+1)#

#=(x^2+25)(x^2-6x+10)#

#=x^4-6x^3+35x^2-150x+250#.

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