Front

What does the Fundamental Theorem of Algebra state?

Back

Every non-constant polynomial function has at least one complex root.

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CCSS.HSN.CN.C.9

Front

How many roots does a polynomial of degree n have?

Back

A polynomial of degree n has exactly n roots, counting multiplicities.

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CCSS.HSN.CN.C.9

Front

What is the degree of a polynomial?

Back

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

Front

If a polynomial has real coefficients, what can be said about its complex roots?

Back

Complex roots must occur in conjugate pairs.

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CCSS.HSN.CN.C.9

Front

What is the relationship between the degree of a polynomial and the number of its zeros?

Back

The degree of a polynomial determines the maximum number of zeros it can have.

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CCSS.HSN.CN.C.9

Front

What is a zero of a polynomial?

Back

A zero of a polynomial is a value of x that makes the polynomial equal to zero.

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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 and its graph.

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CCSS.HSN.CN.C.9

Front

What is the significance of imaginary roots in polynomials?

Back

Imaginary roots indicate that the polynomial does not intersect the x-axis at those points.

Tags

CCSS.HSN.CN.C.9

Front

What is the degree of the polynomial f(x) = x^5 - 3x^3 + x?

Back

The degree of the polynomial is 5.

Front

How do you find the roots of a polynomial function?

Back

You can find the roots by factoring the polynomial, using the quadratic formula, or applying numerical methods.