Question

According to the Fundamental Theorem of Algebra, which polynomial function has exactly 11 roots?

Answer 1

Answer:

According to the Fundamental Theorem of Algebra, a polynomial function of Degree 11 will have exactly 11 roots.

Step-by-step explanation:

According to the Fundamental Theorem of Algebra, the number of roots depends on the Degree of the polynomial.

For example

1. Degree of a Quadratic equation is 2 and it has 2 roots.
2. Degree of a cubic function is 3 and it has 3 roots.

Similarly a Polynomial Function of Degree 11 will have exactly 11 roots.

⇒ All of these roots can be Real

OR

⇒ They can be a mixture of Real Roots and Complex Roots

Note:  But remember that Complex roots always come in Pairs. For example, out of 11 roots , there may be

2 Complex and 9 Real Roots

4 Complex and 7 Real Roots

6 Complex and 5 Real Roots

8 Complex and 3 Real Roots

10 Complex and 1 Real Roots

Or

All the roots will be REAL.