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

1 Answer
George C.
Apr 2, 2016

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

Explanation:

The difference of squares identity can be written:

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

Use this with #a=(x-1)# and #b=2i# as follows:

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

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

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

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

#=x^2-2x+5#

Any polynomial in #x# with these zeros will be a multiple (scalar or polynomial) of this #f(x)#

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