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The minimum degree of a polynomial equation with rational coefficients having $\sqrt{3}+\sqrt{27}, \sqrt{2}+5 i$ as two of its roots is
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Verified Answer
The correct answer is:
6
The polynomial equation with rational coefficients having $\sqrt{3}+\sqrt{27}, \sqrt{2}+5 i$ as two roots. Then, other roots are
$$
\begin{aligned}
& \sqrt{3}-\sqrt{27} \text { and } \sqrt{2}-5 i \\
& -\sqrt{3}+\sqrt{27} \text { and }-\sqrt{3}-\sqrt{27}
\end{aligned}
$$
Therefore, number of roots are 6 and the minimum degree of a polynomial equation having 6 distinct roots is 6 .
$$
\begin{aligned}
& \sqrt{3}-\sqrt{27} \text { and } \sqrt{2}-5 i \\
& -\sqrt{3}+\sqrt{27} \text { and }-\sqrt{3}-\sqrt{27}
\end{aligned}
$$
Therefore, number of roots are 6 and the minimum degree of a polynomial equation having 6 distinct roots is 6 .
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