Question

If 5 and (7+ square root 2) are roots of a polynomial with integer coefficients, what must be another root?

Answer 1

x = 7 -
`√(2)`

Explanation:

note that roots of the form x = a + b
`√(c)` occur in conjugate pairs, that is

x = a - b
`√(c)`

given x = 7 +
`√(2)` is a root then x = 7 -
`√(2)` is the other root