1 / 9

Lesson 76

Lesson 76. Finding polynomial roots. Polynomial roots. Polynomial roots are the solutions of a polynomial equation. These roots are the zeros of the related polynomial function which are the x-intercepts of the graph of the function. Finding roots of a factored polynomial.

hubert
Télécharger la présentation

Lesson 76

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lesson 76 Finding polynomial roots

  2. Polynomial roots • Polynomial roots are the solutions of a polynomial equation. • These roots are the zeros of the related polynomial function which are the x-intercepts of the graph of the function.

  3. Finding roots of a factored polynomial • Find the roots of: • 0 = 2x(x-5)(2x-3) • 2x = 0 x-5 = 0 2x-3 = 0 • x= 0 x = 5 x = 3/2 • Find the roots of: • 0 = -x (x+4)(x- 1/2)

  4. Finding monomial factors to determine zeros • Find the zeros of the polynomial function: • f(x) = 6x3 + 10x2 + 4x • factor GCF 2x(3x2 + 5x +2) • So 2x= 0 , x= 0 • factor 3x2 + 5x +2 using quadratic formula • so zeros are 0, -2,-3

  5. Find the zeros • f(x) = 6x3 + 21x2 + 18x • f(x) = x4 - 3x3 + 2x2 - 6x

  6. Finding binomial factors to determine roots • Find real roots of • 0 = (x+3)(x2+4)-(x+3)(4x+1) • Common factor • 0 = (x+3)(x2+4-(4x+1)) • 0 = (x+3)(x2 -4x +3) • 0 = (x+3)(x-3)(x-1) • So x + 3 = 0 x - 3 = 0 x - 1 = 0 • x = -3 x = 3 x = 1

  7. Find real roots • (x-2)(x2 +2)-(x-2)(4x+7)= 0 • 0 = (x-7)(3x3+4)+(x-7)(5x2 -1) • 0 = (x+4)(2x3 -7)+ (x+4)(5-3x)

  8. Solving polynomial equations • 5x4 = 5x3 - 8x2 -2x • 2x4 = 8x3 - x2 - 13x

More Related