Fundamental Theorem of Algebra Roots/Zeros/X-Intercepts

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Notes 6.6 Fundamental Theorem of Algebra

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Presentation transcript:

Fundamental Theorem of Algebra Roots/Zeros/X-Intercepts L6-5 and L6-6 Obj: Students will find rational roots. Obj: Students will use the Fundamental Theorem of Algebra to solve polynomials Important Terms Rational Numbers Irrational Numbers Fundamental Theorem of Algebra Roots/Zeros/X-Intercepts Rational Root theorem

Find the possible rational roots of 3x3 – x2 – 15x + 5 = 0. Theorems About Roots of Polynomial Equations Find the possible rational roots of 3x3 – x2 – 15x + 5 = 0. Then find the rational roots

Find the roots of 5x3 – 24x2 + 41x – 20 = 0.

Finding Rational Roots 1. x³ + x² - 3x – 3 = 0 Find the roots 2 Finding Rational Roots 1. x³ + x² - 3x – 3 = 0 Find the roots 2. 2x³ - x² + 2x -1 = 0

Obj: Students will use the Fundamental Theorem of Algebra to solve polynomials

By the corollary to the Fundamental Theorem of Algebra, LESSON 6-6 Additional Examples For the equation x4 – 3x3 + 4x + 1 = 0, find the number of complex roots, the possible number of real roots, and the possible rational roots. By the corollary to the Fundamental Theorem of Algebra, x4 – 3x3 + 4x + 1 = 0 has four complex roots. By the Imaginary Root Theorem, the equation has either no imaginary roots, two imaginary roots (one conjugate pair), or four imaginary roots (two conjugate pairs). So the equation has either zero real roots, two real roots, or four real roots. By the Rational Root Theorem, the possible rational roots of the equation are ±1.

Find the number of complex zeros of ƒ(x) = x5 + 3x4 – x – 3. The Fundamental Theorem of Algebra Find the number of complex zeros of ƒ(x) = x5 + 3x4 – x – 3. Find all the zeros.

Find all the zero’s f(x) = x³ + x² -x + 2 y = x³ - 2x² + 4x - 8

Homework 6.5 (p 345) #2-24e 6.6 (p 349) #10-16e 22-26e 32