Question

The minimum degree of a polynomial equation with rational coefficients having $\sqrt{3}+\sqrt{27},\sqrt{2}+5i$ as two of its roots is

• A. 8
• B. 6
• C. 4
• D. 2

Answer 1

Answer: (B)

The polynomial equation with rational coefficients having $\sqrt{3}+\sqrt{27},\sqrt{2}+5i$ as two roots.
Then, other roots are
$\sqrt{3}-\sqrt{27}$ and $\sqrt{2}-5i$
$-\sqrt{3}+\sqrt{27}$ and $-\sqrt{3}-\sqrt{27}$
Therefore, number of roots are $6$ and the minimum degree of a polynomial equation having $6$ distinct roots is $6.$