How do you write a polynomial in standard form given zeros 1 and 2 + 3i?

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Answer 1 · 2016-07-15T17:33:45

#x^2-(3+3i)x+(2+3i)#

A zero, say #a# of a polynomial #f(x)# is one for which #f(a)=0#.

Let us assume that zeros are #{a,b,c,d}#, then it is apparent that such a polynomial could be #(x-a)(x-b)(x-c)(x-d)#.

As we need to write a polynomial with zeros #1# and #2+3i#, the polynomial is

#(x-1)(x-2-3i)# or

#x(x-2-3i)-1(x-2-3i)# or

#x^2-2x-3ix-x+2+3i# or

#x^2-3x-3ix+2+3i# or

#x^2-(3+3i)x+(2+3i)#