Question

The zeroes of a 3rd degree polynomial are 1 and (5 –

i).
Find the remaining zeroes.
-1
:)
-5 + i
no other zeros
5 + i
5+ i
?

Answer 1

5 + i

Explanation:

the Fundamental theorem of Algebra states that a polynomial of gegree n has n zeros , some of which may be complex.

A polynomial of degree 3 will therefore have 3 zeros

given x = 1 and 5 - i are two of the zeros

Complex zeros occur as conjugate pairs , then

5 - i is a zero then 5 + 1 is also a zero

the 3 zeros are x = 1 , x = 5 - i and x = 5 + i