Answer:
x² - 4 x + 3
Step-by-step explanation:
given expression
( x - ( 2 + i ) )( x - ( 2 - i ) )
on solving
= x² - (2 - i )x - (2 + i) x + (2 + i )(2 - i)
= x² - 2 x + i x - 2 x - i x + 2² - i²
using identity
(a+ b)(a-b) = a² - b²
= x² - 4 x + 2 - (-1) ∵ i² = -1
= x² - 4 x + 2 + 1
= x² - 4 x + 3
hence, the required polynomial equation is x² - 4 x + 3
