Question

If 5 and (5+ square root 5) are two of the

roots of a third degree polynomial with integer coefficients, what is the other root?

Answer 1

5 -
`√(5)`

Explanation:

a polynomial of degree 3 has 3 roots

radical roots occur in conjugate pairs.

given 5 +
`√(5)` is a root then 5 -
`√(5)` is also a root.

the 3 roots are therefore

x = 5 and x = 5 ±
`√(5)`