# Find the polynomial g(x) with integer coefficients of least degree (and positive leading coefficients as small as possible) for which 1-2i is a double root?

##### 1 Answer

Oct 5, 2017

#### Explanation:

As the polynomial **double root** of the polynomial, it has its factor

But it will give us complex coefficients and hence for integers as coefficients we must have another **double root** which is complex conjugate of

Hence the polynomial with least degree would be

=

=

=

=

=

(using

#(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2ab# )

=