# How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are 4, 4, 2+i?

##### 1 Answer

Sep 17, 2017

#### Explanation:

Assuming you want a polynomial with real coefficients, the complex conjugate

#f(x) = (x-4)(x-4)(x-(2+i))(x-(2-i))#

#color(white)(f(x)) = (x^2-8x+16)((x-2)+i)((x-2)-i)#

#color(white)(f(x)) = (x^2-8x+16)((x-2)^2-i^2)#

#color(white)(f(x)) = (x^2-8x+16)(x^2-4x+4+1)#

#color(white)(f(x)) = (x^2-8x+16)(x^2-4x+5)#

#color(white)(f(x)) = x^4-12x^3+53x^2-104x+80#

Any polynomial in