What is the lowest possible degree of the polynomial that has 5, √5 and 5i as three of its zeros?

Question

a. 3   b. 5  c. 6  d.7

Answer 1

Assuming the polynomial requires

rational coefficients, the degree must be 5

 

because sqrt(5) is a root, then so is -sqrt(5)

 

because 5i is a root, then so is -5i

 

Note that if irrational coefficients are allowed , then the

degree CAN be 4 but that is not one of your choices

as an answer.

 

5