Help me please!! An emergency!! A polynomial equation with rational coefficients has the roots 5, sqrt6, 3, -sqrt7. Find two ad

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!

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Nho 2 weeks 2021-08-28T18:22:53+00:00 1 Answers 0 views 0

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    2021-08-28T18:24:02+00:00

    Given:

    A polynomial equation with rational coefficients has the roots   5, \sqrt{6}, 3, -\sqrt{7}.

    To find:

    The two additional roots.

    Solution:

    According to the irrational root theorem, if a+\sqrt{b} is a root of a polynomial, then a-\sqrt{b} is also the root of that polynomial.

    It is given that, \sqrt{6}\text{ and }-\sqrt{7} are roots of a polynomial.

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

    Therefore, the two additional roots are -\sqrt{6}\text{ and }\sqrt{7}.

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