The minimum degree of a polynomial equation with rational coefficients having $\sqrt{3}+\sqrt{27},…
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
8
6
4
2
Solution
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