## evy15 2 years ago Find all zeros 5x^5-20x^4-40x^3-16x^2-45x+180=0

1. evy15

@zepp

What do you mean by "Find all zeros" ?

3. evy15

find the zeros of th eq

4. wio

Use rational root theorem to find first zero. Then use synthetic division to factor it out.

5. mark_o.

hi @evy15 are you in numerical analysis? the root are -2.07316, 1.2355, 5.5573 and two complex roots check it for yourself if they are true

6. matricked

@evy though the equation is 5x^5-20x^4-40x^3-16x^2-45x+180=0 correct bu t may be i feel u have typed in -16X^2 instead of 160x^2

7. evy15

no its correct

8. evy15

9. evy15

can someone respond

10. mathmate

Have you done numerical methods in your course? This is not a problem that can be solved by factorization, or rearrangements. I suggest you triple check the question.

11. evy15

its correct can you tell me how to begin

12. mathmate

It can be solved numerically, or graphically. Are these expected methods to use in your course?

13. evy15

yes the thing is i missed a day in class and now i dont know how to work this out

14. mathmate

Are you working on factorization, Descartes rule of signs, etc.? I suggest you check your course outline to see what you're expected to know, or check with a friend to see what has been done that day. The prof would also be pleased to tell you what has been covered that day. This problem requires numerical methods which are techniques completely different from your previous problems.

15. evy15

can u help me and explain it to me

16. evy15

i have tried to use the book but i keep getting it wrong

17. mathmate

What is the name of your math course?

18. evy15

Algebra 2

19. mathmate

Then there is probably another typo in the question.

20. evy15

21. mathmate

I believe you, but your prof made a typo! Check in the index of your textbook to see if Newton's method is in there. What is the title of your textbook?

22. evy15

ok

23. evy15

Im not sure, hold on

24. evy15

Holt McDougal Larson Algebra 2

25. mathmate

Can you find "Newton's method" in the index?

26. mathmate

On which chapter are you working?

27. mathmate

Is it paper home-work or online?

28. evy15

its a take home test and i couldnt find it

29. mathmate

As matricked pointed out, IF -16x^2 had been +160x^2, then there are rational roots obtainable by grouping. 5x^5-20x^4-40x^3+160x^2-45x+180 =5(x^5-4x^4-8x^3+32x^2-9x+36) \(= 5( x^4(x-4) -8x^2(x-4) -9(x-4)) \) \(= 5(x-4)(x^4-8x^2-9) \) \(= 5(x-4)(x^2-9)(x^2+1) \) \(= 5(x-4)(x+3)(x-3)(x^+1) \)

30. mathmate

*last factor is \( (x^2+1) \)

31. evy15

ok do you solve for them now

32. evy15

hold on a second, im sorry