Finding Zeros of Polynomials Flashcard

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What are the zeros of a polynomial?

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The zeros of a polynomial are the values of x for which the polynomial evaluates to zero. They are also known as the roots of the polynomial.

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CCSS.HSF-IF.C.7C

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State the Fundamental Theorem of Algebra.

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The Fundamental Theorem of Algebra states that every non-constant polynomial equation of degree n has exactly n complex roots, counting multiplicities.

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CCSS.HSN.CN.C.9

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How do you find the zeros of a polynomial function?

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To find the zeros of a polynomial function, set the polynomial equal to zero and solve for x using factoring, the quadratic formula, or numerical methods.

Tags

CCSS.HSF-IF.C.7C

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What is a rational zero?

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A rational zero is a solution to a polynomial equation that can be expressed as a fraction p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

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CCSS.HSA.APR.B.2

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

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The degree of a polynomial indicates the maximum number of zeros it can have. A polynomial of degree n can have up to n zeros.

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

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Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor (x - c). It helps in finding zeros by testing possible rational roots.

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CCSS.HSA.APR.D.6

Front

What is the significance of the discriminant in a quadratic equation?

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The discriminant (b² - 4ac) determines the nature of the roots of a quadratic equation: if positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

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CCSS.HSA-REI.B.4B

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How can you verify if a number is a zero of a polynomial?

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To verify if a number c is a zero of a polynomial p(x), substitute c into the polynomial. If p(c) = 0, then c is a zero.

Tags

CCSS.HSF-IF.C.7C

Front

What is the Rational Root Theorem?

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The Rational Root Theorem provides a way to find all possible rational roots of a polynomial equation by listing the factors of the constant term and the leading coefficient.

Tags

CCSS.HSA.APR.B.2

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What does it mean for a zero to have multiplicity?

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A zero has multiplicity if it is a root of the polynomial more than once. For example, if (x - 2)² is a factor, then x = 2 is a zero with multiplicity 2.

Tags

CCSS.HSF-IF.C.7C