Flashcard 6.7

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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.

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How do you determine the number of complex roots for a polynomial?

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The number of complex roots of a polynomial is equal to its degree. For example, a polynomial of degree 5 has 5 complex roots.

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What is a polynomial equation?

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A polynomial equation is an equation that involves a polynomial expression, which is a sum of terms, each consisting of a variable raised to a non-negative integer power multiplied by a coefficient.

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The polynomial has 5 complex roots.

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What is the process to solve a cubic equation algebraically?

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To solve a cubic equation algebraically, you can use methods such as factoring, synthetic division, or applying the cubic formula.

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What is the significance of the discriminant in polynomial equations?

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The discriminant helps determine the nature of the roots of a polynomial. A positive discriminant indicates distinct real roots, zero indicates a repeated real root, and a negative discriminant indicates complex roots.

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What is a complex root?

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A complex root 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.

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What is the degree of a polynomial?

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