Exploring the Fundamental Theorem of Algebra

What does the Fundamental Theorem of Algebra state about an nth-degree polynomial?

• It has at most n roots.

• It has no roots.

• It has at least n roots.

• It has exactly n roots.

How many roots does a second-degree polynomial have according to the Fundamental Theorem of Algebra?

• One

• Two

• Three

• Four

What shape does the graph of a second-degree polynomial typically form?

• Line

• Circle

• Parabola

• Ellipse

How many real roots does a third-degree polynomial typically have?

• One

• Three

• Two

• Four

What type of roots does a second-degree polynomial have if it does not intersect the x-axis?

• Two real roots

• One real root

• No roots

• Two complex roots

What is a key extension of the Fundamental Theorem of Algebra?

• It excludes complex coefficients.

• It includes complex roots.

• It applies only to linear polynomials.

• It only applies to real roots.

How do complex roots typically appear in polynomials?

• In pairs

• In quadruples

• In triples

• As single roots

Can a third-degree polynomial have three non-real complex roots?

• Yes

• No

• Only if it has real coefficients

• Sometimes

How many pairs of complex roots can a fourth-degree polynomial have?

• Four

• Three

• Two

• One

What is the relationship between real numbers and complex numbers in the context of polynomial roots?

• Complex numbers are a subset of real numbers.

• They are identical sets.

• Real numbers are a subset of complex numbers.

• They are completely separate sets.