Features of Polynomials

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What is a polynomial?

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What is the degree of a polynomial?

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What does it mean for a root to have a multiplicity?

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

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The number of real roots of a polynomial can be determined using the Fundamental Theorem of Algebra, which states that a polynomial of degree n has exactly n roots (real or complex). The nature of these roots can be analyzed using the discriminant.

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

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The degree of a polynomial indicates the maximum number of roots it can have. For example, a polynomial of degree 4 can have up to 4 roots, which can be real or complex.

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What is a factor of a polynomial?

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What is the significance of imaginary roots in polynomials?

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Imaginary roots occur in conjugate pairs in polynomials with real coefficients. If a polynomial has an imaginary root, it must also have its conjugate as a root.

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How can you find the roots of a polynomial?

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Roots of a polynomial can be found using various methods such as factoring, synthetic division, the Rational Root Theorem, or numerical methods like the Newton-Raphson method.

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What is the standard form of a polynomial?

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What is the difference between a polynomial and a rational function?

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