Question

Describe the roots of the polynomial, 3x4+ 5x3 +8x²-6x+1 using the descriptions

below:
1. How many roots?
2. How many are real?
3. How many are imaginary?
4. What are the multiplicity of each root?
O There are 2 real roots with multiplicity of 2 each
O There are 4 real roots with multiplicities of 1 each
O There are 2 real roots and 2 imaginary roots; all roots have a multiplicity of 1 each
O There are 4 imaginary roots with multiplicities of 1 each

Answer 1

The polynomial 3x^4 + 5x^3 + 8x^2 - 6x + 1 has the following descriptions for its roots

How many roots?

The polynomial is of degree 4, so it has a total of 4 roots.

How many are real?

The polynomial has only real coefficients, so it may have real roots.

How many are imaginary?

Since the polynomial has real coefficients and an even degree, it is possible to have imaginary roots.

What are the multiplicities of each root?

O There are 2 real roots and 2 imaginary roots; all roots have a multiplicity of 1 each. This means that out of the four roots, two of them are real and two are imaginary. Additionally, each root has a multiplicity of 1, indicating that none of the roots are repeated or have a higher multiplicity.