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

$x^2-2x+1+4$

$x^2-2x+5$