# How do you find the quadratic equation with roots at (2-i) and its complex conjugate?

##### 1 Answer

Jan 9, 2016

Multiply out

#x^2-4x+5 = 0#

#### Explanation:

The Complex conjugate of

Multiply out

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

with

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

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

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

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

#=x^2-4x+5#