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

Sagot :

stigawithfun

Answer:

[tex]-\sqrt{2}[/tex] and [tex]\sqrt{13}[/tex]

Step-by-step 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 + [tex]\sqrt{3}[/tex], 3 and 4 - 3i, then 2 - [tex]\sqrt{3}[/tex], and 4 + 3i are also roots of the polynomial.

Therefore, since the given polynomial has rational coefficients and some of its roots are , [tex]\sqrt{2}[/tex] and  - [tex]\sqrt{13}[/tex], then -[tex]\sqrt{2}[/tex] and [tex]\sqrt{13}[/tex] are also roots of the polynomial.

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