How do you write a polynomial function of least degree that has real coefficients, the following given zeros 2, -1+i, -1-i?

1 Answer
Aug 9, 2016

Answer:

#f(x)=x^3-2x-4#

Explanation:

Each zero corresponds to a linear factor.

So we can write:

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

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

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

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

#=x^3-2x-4#

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