Holt McDougal Algebra 2 Fundamental Theorem of Algebra How do we use the Fundamental Theorem of Algebra and its corollary to write a polynomial equation.

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Presentation transcript:

Holt McDougal Algebra 2 Fundamental Theorem of Algebra How do we use the Fundamental Theorem of Algebra and its corollary to write a polynomial equation of least degree with given roots? How do we identify all of the roots of a polynomial equation?

Holt McDougal Algebra 2 Fundamental Theorem of Algebra Using the Fundamental Theorem of Algebra, you can write any polynomial function in factor form. To find all roots of a polynomial equation, you can use a combination of the Rational Root Theorem, the Irrational Root Theorem, and methods for finding complex roots, such as the quadratic formula.

Holt McDougal Algebra 2 Fundamental Theorem of Algebra Example 1: Finding All Roots of a Polynomial Solve x 4 – 3x 3 + 5x 2 – 27x – 36 = 0 by finding all roots. The polynomial is of deg. 4, so there are four roots for the equation.

Holt McDougal Algebra 2 Fundamental Theorem of Algebra Example 2: Finding All Roots of a Polynomial Solve x 4 + 4x 3 – x 2 +16x – 20 = 0 by finding all roots. The polynomial is of deg. 4, so there are four roots for the equation.

Holt McDougal Algebra 2 Fundamental Theorem of Algebra Lesson 4.2 Practice B