How do you write a polynomial with zeros 3-i, 5i and leading coefficient 1?

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Answer 1 · 2016-10-23T11:50:10

#x^4-6x^3+35x^2-150x+250=0#

For polynomial equations with real coefficients, complex roots occur

in conjugate pairs. so, the least-degree polynomial equation having

roots #3 +-i and +-5i# is

#(x-3-i)(x-3+i)(x-5i)(x+5i)=0# that simplifies to

#((x-3)^2+1)(x^2+25)=0# and this expands to

#x^4-6x^3+35x^2-150x+250=0#

.