Question

A polynomial P(x) has rational coefficients. Name additional roots p(x) given the roots 5+sqrt 3 and - sqrt 2

Answer 1

irrational roots of such a polynomial come in conjugate pairs
so if \(a+\sqrt{b}\) is a root, so is \(a-\sqrt{b}\)

Answer 2

I'm still confused

Answer 3

these are called "conjugates"
the conjugate of \(a+\sqrt{b}\) is \(a-\sqrt{b}\)
what, therefore, is the conjugate of \(5+\sqrt{3}\)?

Answer 4

5-sqrt3

Answer 5

yes, so that must be another root

Answer 6

what about the conjugate of \(-\sqrt{2}\)?
hint, it is the same as \(0-\sqrt{2}\)

Answer 7

sqrt2

Answer 8

yes, so you have the answer

Answer 9

thanx so much!!!!!

Answer 10

yw