Question

Help me please!! An emergency!!

A polynomial equation with rational coefficients has the roots 5, sqrt6, 3, -sqrt7. Find two additional roots.

Thank you!

Answer 1

Given:

A polynomial equation with rational coefficients has the roots
`5, √(6), 3, -√(7)`.

To find:

The two additional roots.

Solution:

According to the irrational root theorem, if
`a+√(b)` is a root of a polynomial, then
`a-√(b)` is also the root of that polynomial.

It is given that,
`√(6)\text{ and }-√(7)` are roots of a polynomial.

By using irrational root theorem,
`-√(6)\text{ and }√(7)` are also the roots of that polynomial.

Therefore, the two additional roots are
`-√(6)\text{ and }√(7)`.