## evy15 2 years ago Find the roots of the polynomial eq. x^3-3x^2-5x-15=0

1. mathmate

Are you familiar with Descarte's rule of signs?

2. mathmate

Using Descartes rule of signs, we know that there is one positive real root, and either two negative real roots, or two complex roots.

3. evy15

no ive neve used it

4. evy15

never

5. mathmate

What have you been using to calculate the root of a polynomial equation that does not have rational roots? There is one more thing you could do, double-check the question. This polynomial does not have rational roots.

6. dpaInc

maybe a numerical method to find the roots?

7. mathmate

I agree,... if the question had been correctly posted.

8. dpaInc

or graphing calculator?

9. KingGeorge

I would go out on a limb, and say that this isn't the correct equation. Some slight sign changes result in an easily factored equation.

10. mathmate

True, that is for getting an initial estimate.

11. mathmate

@evy15 we're waiting anxiously your confirmation of the equation!! :)

12. dpaInc

agree... check that last term... should it really be -15 ???

13. evy15

yes the equation is correct

14. mathmate

As @dpalnc said, if the last term is +15, then there are three rational roots (i.e. the equation can be factorized and solved with 3 real rational roots).

15. evy15

`no its negative

16. mathmate

In that case, you have 2 complex roots and a real irrational root. What methods have you used so far to solve for irrational roots?

17. mathmate

Cubics can be solved using Cardano's formula, which is overly complex. We can usually find the real root using a numerical method. Does all this sound familiar to you?

18. wio

@evy15 Is this homework? Are there certain methods you are supposed to be learning?

19. wio

Once you find the 1st root, you can use synthetic division an the quadratic equation to find the other two.

20. evy15

is it -3

21. wio

The rational root theorem says that it's got to be $\pm\frac{1,3,5,15}{1}$So $$-3$$ is a possibility. Try plugging it in.

22. KingGeorge

Are you absolutely sure that you didn't type it incorrectly? With a small sign change, one of the roots is indeed -3. However, as written, it has one irrational root, and two complex roots.

23. evy15

the thing is im completely confused because I missed a day in class and now idk how to do it

24. evy15

its typed in correctly

25. joemath314159

I checked the solutions to the equation in wolfram, they are pretty intense. If you didnt type the problem incorrectly, then the teacher/professor typed it incorrectly, because there is no way a teacher should expect a student to find those roots by hand =/

26. KingGeorge

I agree^^

27. joemath314159

and like others have mentioned, if only one of the signs is changed, it becomes an easy regular standard problem.

28. KingGeorge

Unless, of course, you're learning about methods to approximate roots.

29. joemath314159

oh yeah. that could be the case. Newtons Method :)

30. evy15

its typed correctly

31. evy15

32. dpaInc

the only way i can think of if the equation is correct as you say is to approximate the root(s) using newton's method...

33. dpaInc

or graphing calc. or wolfram.

34. evy15

on calculator I got -15

35. joemath314159

If the problem as typed is correct, there is nothing we (or anyone) can do. Not without a calc or comupter, or something.

36. dpaInc

try to see if x=-15 is a root by plugging that back into the original equation... i don't think that's right.

37. dpaInc

wait... do you mean to find the y-intercept of $$\large y=x^3-3x^2-5x-15$$ ?? because -15 is the y-intercept...

38. joemath314159

if thats the actual problem....then lol.

39. evy15

ok thanks

40. dpaInc

ho boy...

41. mathmate

Isn't the question: "Find the roots of the polynomial eq. x^3-3x^2-5x-15=0"

42. evy15

yes

43. mathmate

So you need the roots of the equation, not just the y-intercept. As I said in the other post, from the type of question you have, it seems likely that either you or your prof had a typo in this question. To make sure it'd better be your prof, you want to triple check for typos in your post.