1 / 30

Answers to homework

Answers to homework. 65) Zeros are 2 and ≈±2.236 B) x= 2 c) f(x)=(x-2)(x-√5)(x+√5) 78) f(x)= (x-2)x²+5 = x³-2x²+5 B) = -(x+3)x²+1 = -x³-3x²+1 93) f(x) = x³-7x²+12x 94) f(x) = x²+5x-6 95) f(x)= x³ + x² - 7x -3 96) f(x) = x^4 -3x³-5x²+9x-2. 2.5 Zeros of Polynomial Functions.

matia
Télécharger la présentation

Answers to homework

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. Answers to homework

  2. 65) Zeros are 2 and ≈±2.236 • B) x= 2 c) f(x)=(x-2)(x-√5)(x+√5) • 78) f(x)= (x-2)x²+5 = x³-2x²+5 • B) = -(x+3)x²+1 = -x³-3x²+1 • 93) f(x) = x³-7x²+12x • 94) f(x) = x²+5x-6 • 95) f(x)= x³ + x² - 7x -3 • 96) f(x) = x^4 -3x³-5x²+9x-2

  3. 2.5 Zeros of Polynomial Functions

  4. Zeros of Polynomial Functions • a) The first degree polynomial f(x)= x-2 has exactly one zero x=2 • b) counting multiplicity, the second-degree polynomial function f(x)=x²-6x+9=(x-3)(x-3) has exactly two zeros: x=3 and x=3.this is called a repeated zero)

  5. d)The fourth-degree polynomial function • f(x)= x^4-1=(x-1)(x+1)(x-i)(x+i) • Has exactly four zeros: x=1, x=-1, x=i, x=-i c) The third-degree polynomial function f(x)=x³+4x=x(x²+4)=x(x-2i)(x+2i) Has exactly three zeros: x=0, x=2i, and x=-2i

  6. The Rational Zero Test • Rational zero = p/q • Where p and q have no common factors other than 1, and • p = a factor of the constant term • q= a factor of the leading coefficient • Possible rational zeros= • Factors of constant term/factors of leading coefficient.

  7. Rational Zero Test with leading coefficient of 1 • Find the rational zeros of: • the factors of 1 are 1 and -1, use synthetic division

  8. Try this • Find all rational zeros of the function:

  9. 1st list all of the factors ±1, ±2, ±3, ±6 • Try one factor using synthetic division if it does not work try another.

  10. Answers are 1,2,3

  11. With so many possibilities(32 in fact), it is worth your time to stop and graph the polynomial equation. This will shorten your list of possible zeros. Use synthetic division to term the final roots. Answer is x=2

  12. Try this • Find all real solutions of the polynomial equation

  13. List all possible factors of 6 and 2 • ±1, ±2, ±3, ±6 divide by ±1, ±2 • Use synthetic divisions to find factors.

  14. Answer • -6, 1, ½

  15. Homework: • P 179-180 # 3-9 odd, 13, 19, 21, 25, 29

  16. Answers to homework • 3) 2, -4 • 5) -6, ±I • 7)±1, ±3 • 9) ±1, ±3, ±5, ±9, ±15, ±45, ±1/2, ±3/2, ±5/2,±9/2, ±15/2, ±45/2 • 13) 1, -1, 4 • 19) -2, 3, ±2/3

  17. 21) -1, 2 • 25) ±1, ±2,±4 c) -2, -1, 2 • 29) ±1, ±2, ±4, ±8, ±1/2 c) -1/2, 1, 2, 4

  18. Conjugate pairs: If a+bi is one answer a-bi is also an answer.

  19. Find all the zeros:

  20. Try this

  21. Try This • Use Descarte’s Rule of Signs to determine the possible numbers of positive and negative zeros of the function:

  22. Homework • P180 #48, 50, 51, 54, 82, 83, 85

More Related