Front

What does the Fundamental Theorem of Algebra state?

Back

Every non-constant polynomial function of degree n has exactly n roots in the complex number system, counting multiplicities.

Tags

CCSS.HSN.CN.C.9

Front

How many roots does a polynomial of degree 3 have according to the Fundamental Theorem of Algebra?

Back

A polynomial of degree 3 has exactly 3 roots in the complex number system.

Tags

CCSS.HSN.CN.C.9

Front

What is a root of a polynomial?

Back

A root of a polynomial is a value of x for which the polynomial evaluates to zero.

Tags

CCSS.HSF-IF.C.7C

Front

What is the Rational Root Theorem?

Back

The Rational Root Theorem states that any rational solution of a polynomial equation, in the form of p/q, is such that p is a factor of the constant term and q is a factor of the leading coefficient.

Tags

CCSS.HSA.APR.B.2

Front

If a polynomial has a degree of 5, how many zeros does it have?

Back

It has exactly 5 zeros, counting multiplicities.

Tags

CCSS.HSN.CN.C.9

Front

What are complex roots?

Back

Complex roots are solutions to polynomial equations that include imaginary numbers, typically in the form a + bi, where a and b are real numbers.

Tags

CCSS.HSN.CN.C.9

Front

What is the significance of multiplicity in polynomial roots?

Back

Multiplicity refers to the number of times a particular root is repeated in a polynomial. A root with a higher multiplicity indicates that the polynomial touches the x-axis at that root.

Tags

CCSS.HSF-IF.C.7C

Front

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

Back

You can determine the number of real roots by analyzing the polynomial's degree, its discriminant, and using techniques such as synthetic division or graphing.

Front

What is synthetic division and how is it used in finding roots?

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor, helping to find roots more efficiently.

Tags

CCSS.HSA.APR.D.6

Front

What is the relationship between the coefficients of a polynomial and its roots?

Back

The coefficients of a polynomial are related to its roots through Vieta's formulas, which express the sums and products of the roots in terms of the coefficients.

Tags

CCSS.HSN.CN.C.9