How do you write a polynomial function with minimum degree whose zeroes are 1-2i and 1+2i?

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Answer 1 · 2017-01-05T18:31:24

#f(x)=x^2-2x+5#

The requested polynomial function is:

#f(x)=(x-(1-2i))(x-(1+2i))#

that's:

#(x-1+2i)(x-1-2i)#

Since

#(a+b)(a-b)=a^2-b^2#

you get

#(x-1)^2-4i^2#

Since

#(a+b)^2=a^2+2ab+b^2#

and

#i^2=-1#

you get

#x^2-2x+1+4#

#x^2-2x+5#