Complex Zeros Practice

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What is a complex zero?

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A complex zero is a solution to a polynomial equation that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit.

Tags

CCSS.HSN.CN.C.9

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What is the Conjugate Root Theorem?

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The Conjugate Root Theorem states that if a polynomial has real coefficients and a complex zero a + bi, then its conjugate a - bi is also a zero of the polynomial.

Tags

CCSS.HSN.CN.C.9

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How do you determine the number of real zeros in a polynomial?

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The number of real zeros can be determined using the Fundamental Theorem of Algebra, which states that a polynomial of degree n has exactly n zeros (real or complex), and by analyzing the polynomial's graph.

Tags

CCSS.HSN.CN.C.9

Front

What is 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.

Tags

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 the variable using factoring, synthetic division, or the quadratic formula.

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What is a polynomial function of least degree?

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A polynomial function of least degree is the simplest polynomial that has the given zeros, meaning it has the lowest possible degree while still containing all specified roots.

Tags

CCSS.HSF-IF.C.7C

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What are rational zeros?

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Rational zeros are solutions 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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How do you apply the Rational Root Theorem?

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The Rational Root Theorem helps identify possible rational zeros of a polynomial by listing all possible fractions formed by the factors of the constant term and the leading coefficient.

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CCSS.HSA.APR.B.2

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What is the significance of the degree of a polynomial?

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The degree of a polynomial indicates the highest power of the variable, which determines the number of zeros and the behavior of the polynomial's graph.

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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 is a zero of a polynomial, substitute the number into the polynomial equation. If the result is zero, then it is a zero.

Tags

CCSS.HSF-IF.C.7C