Given:
Degree of a polynomial is 7.
To find:
The possible combination of root types for a 7th degree polynomial.
Solution:
We know that, by complex conjugate root theorem, is a complex number is a root of a polynomial, then its conjugate is also the root of that polynomial, it means number of complex roots always an even number.
Similarly,
Irrational roots are also occurs in pairs. If [tex]1+\sqrt{2}[/tex] is a root of polynomial, then its [tex]1-\sqrt{2}[/tex] is also the root of that polynomial, it means number of irrational roots always an even number.
In options A, B and C either complex or irrational roots are odd, which is not true.
Therefore, the correct option is D.
