Which is a possible combination of root types for a 7th degree polynomial? Which is a possible combination of root types for a 7th degree polynomial?
6 rational roots, 1 irrational root
3 irrational roots, 4 complex roots
2 rational roots, 2 irrational roots, 3 complex roots
7 rational roots

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 is a root of polynomial, then its 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.

the answer is b: 18

step-by-step explanation:

use the pythagorean theorem to .

a^2+b^2=c^2

plug 18 for "r"

the 2 legs are 18 and 24

18^2+24^2=c^2

324+576=c^2

900=c^2

c=30

30-12=18

18 is the radius

: )