What is a polynomial function for 5, i, -i?

1 Answer
Sep 19, 2016

Answer:

#f(x)=x^3-5x^2+x-5#

Explanation:

I have assumed that #{5,i,-i}# are intended to be the zeros of the function.

In this case, the function can be factored as:
#color(white)("XXX")(x-5)((x-i)(x+i)#

#color(white)("XXX")=(x-5)(x^2-i^2)#

#color(white)("XXX")=(x-5)(x^2+1)#

#color(white)("XXX")=x^3+x -5x^x-5#

(or in standard polynomial form)
#color(white)("XXX")=x^3-5x^2+x-5#