Real and Imaginary Roots of Polynomials

Front

What is the factored form of a polynomial with roots 2, 5i, and 6?

Back

(x-6)(x-2)(x+5i)(x-5i)

Front

How many imaginary roots can a polynomial of degree 6 have?

Back

4

Front

What is the least degree of a polynomial that has 4 real roots and 2 complex roots?

Back

6

Front

If 2i is a zero of a polynomial, what other zero must also be present?

Back

-2i must also be a zero.

Front

What is the degree of a polynomial with 4 real roots and 2 complex roots?

Back

6

Front

What is the relationship between real and imaginary roots in polynomials?

Back

Complex roots occur in conjugate pairs, so if a polynomial has an imaginary root, its conjugate is also a root.

Front

What is the maximum number of real roots a polynomial of degree n can have?

Back

A polynomial of degree n can have at most n real roots.

Front

What is the significance of the Fundamental Theorem of Algebra?

Back

It states that every non-constant polynomial has at least one complex root.

Front

How do you determine the number of real roots of a polynomial?

Back

By analyzing the polynomial's degree and the nature of its coefficients, or using methods like Descartes' Rule of Signs.

Front

What is a polynomial's degree?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.