Question

Rewrite each expression as a polynomial in standard form(x-(2+i))(x-(2-i))

Answer 1

x² - 4 x + 3

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