6-8 Roots and Zeros – Day 1 SWBAT

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Presentation transcript:

6-8 Roots and Zeros – Day 1 SWBAT determine the number and type of roots for a polynomial equation. Find the zeros of a polynomial function. Holt McDougal Algebra 2 Holt Algebra 2

Notes: - pg 362

1. Graphs of an Equation Zeros: x = -2, -1, 1, 2 Factors: List the factors and zeros of the graph. Zeros: x = -2, -1, 1, 2 Factors: (x + 2)(x + 1)(x – 2)(x – 1)

Determine the number of roots. x2 – 8x + 16 = 0 x = 4  double root One real repeated root 4 has a multiplicity of 2 x4 – 1 = 0 x = + i , + 1 Two real roots, 2 imaginary roots

Try on your own: Pg 363 # 1A, 1B

Notes: Notice that the degree of the function is the same as the number of zeros. This is true for all polynomial functions. However, all of the zeros are not necessarily real zeros. Polynomials functions, like quadratic functions, may have complex zeros that are not real numbers. For example: 2x2 + 4x + 1 has 2 roots 3x4 + 1 has 4 roots

HOMEWORK Pg 366 #s 11-16 all