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A polynomial function P(x) with rational coefficients has the roots sqrt 2 and - sqrt 13. Find two additional roots.

1 Answer

6 votes

Answer:


-√(2) and
√(13)

Explanation:

Given a polynomial with rational coefficients, its irrational and complex roots would occur in conjugate pairs.

For example, if the roots of a polynomial are 2 +
√(3), 3 and 4 - 3i, then 2 -
√(3), and 4 + 3i are also roots of the polynomial.

Therefore, since the given polynomial has rational coefficients and some of its roots are ,
√(2) and -
√(13), then -
√(2) and
√(13) are also roots of the polynomial.

User Dertom
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