Understanding Complex Roots and Polynomials

Rachel introduces the fundamental theorem of algebra, explaining its importance in determining the number of roots a polynomial has, including real and complex roots. She emphasizes that the theorem does not specify the roots but indicates how many to find. Rachel provides examples to illustrate how the degree of a polynomial determines the number of roots and discusses the need to reorder polynomials to identify the highest exponent.

What is the primary significance of the fundamental theorem of algebra?

• It tells you the exact roots of a polynomial.

• It indicates the number of roots a polynomial has.

• It shows where the polynomial crosses the axis.

• It provides the sum of the roots.

According to the fundamental theorem of algebra, what does the theorem not tell you?

• The number of roots a polynomial has.

• The exact roots of the polynomial.

• The degree of the polynomial.

• The type of roots present.

What does the fundamental theorem of algebra help you find after knowing the number of roots?

• The degree of the polynomial.

• The sum of the roots.

• The exact location of the roots.

• The roots themselves.

What is the role of the fundamental theorem of algebra in graphing polynomials?

• It provides the slope of the graph.

• It helps in finding the exact points of intersection.

• It shows where the graph crosses the axis.

• It indicates the number of times the graph crosses the axis.

What types of roots are included in the total number of roots according to the theorem?

• Neither real nor complex roots.

• Both real and complex roots.

• Only complex roots.

• Only real roots.

What is a key characteristic of complex roots?

• They always come in pairs.

• They are always real numbers.

• They are always greater than real roots.

• They are always less than real roots.

How many roots does a polynomial of degree 6 have?

• 6

• 3

• 12

• 5

What is the highest exponent in the polynomial 12x^6 + 5x + 4?

• 4

• 5

• 12

• 6

In the polynomial 5n + 3n^2 + 2, what is the degree of the polynomial?

• 2

• 3

• 1

• 5

What must be done to a polynomial to determine its degree?

• Multiply all the terms.

• Add all the coefficients.

• Order the terms by their exponents.

• Subtract the smallest exponent from the largest.