1 / 5

EXAMPLE 2

STEP 1. Find the rational zeros of f . Because f is a polynomial function of degree 5 , it has 5 zeros. The possible rational zeros are + 1, + 2, + 7, and + 14 . Using synthetic division, you can determine that – 1 is a zero repeated twice and 2 is also a zero. STEP 2.

lisabarnes
Télécharger la présentation

EXAMPLE 2

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. STEP 1 Find the rational zeros of f. Because fis a polynomial function of degree 5, it has 5 zeros. The possible rational zeros are + 1, + 2, + 7, and +14. Using synthetic division, you can determine that – 1 is a zero repeated twice and 2 is also a zero. STEP 2 Write f (x) in factored form. Dividing f (x) by its known factors x + 1, x + 1, and x – 2 gives a quotient of x2– 4x + 7. Therefore: EXAMPLE 2 Find the zeros of a polynomial function Find all zeros of f (x) = x5 – 4x4 + 4x3 + 10x2 – 13x – 14. SOLUTION f (x) = (x + 1)2(x – 2)(x2 – 4x + 7)

  2. STEP 3 Find the complex zeros of f . Use the quadratic formula to factor the trinomial into linear factors. f(x) = (x + 1)2(x – 2) x – (2 + i 3 ) x – (2 – i 3 ) ANSWER The zeros of f are – 1, – 1, 2, 2 + i 3 , and2 – i 3. EXAMPLE 2 Find the zeros of a polynomial function

  3. Find the rational zero of f. because f is a polynomial function degree 3, it has 3 zero. The possible rational zeros are 1 , 3, using synthetic division, you can determine that 3 is a zero reputed twice and –3 is also a zero STEP 1 STEP 2 Writef (x) in factored form + + – – for Example 2 GUIDED PRACTICE Find all zeros of the polynomial function. 3. f (x) = x3 + 7x2 + 15x + 9 SOLUTION Formula are (x +1)2 (x +3) f(x) = (x +1) (x +3)2 The zeros of f are – 1 and – 3

  4. Find the rational zero of f. because f is a polynomial function degree 5, it has 5 zero. The possible rational zeros are 1 , 2, 3 and Using synthetic division, you can determine that 1 is a zero reputed twice and –3 is also a zero STEP 1 6. STEP 2 Writef (x) in factored formdividing f(x)by its known factor (x – 1),(x – 1)and (x+2) given a qualitiesx2 – 2x +3 therefore + + + + – – – – for Example 2 GUIDED PRACTICE 4. f (x) = x5– 2x4 + 8x2– 13x + 6 SOLUTION f (x) = (x – 1)2 (x+2) (x2 – 2x + 3)

  5. STEP 3 Find the complex zero of f. use the quadratic formula to factor the trinomial into linear factor f (x) = (x –1)2 (x + 2) [x – (1 + i 2) [ (x – (1 – i 2)] Zeros of f are 1, 1, – 2, 1 + i 2 , and 1 – i 2 for Example 2 GUIDED PRACTICE

More Related