anonymous
  • anonymous
Find the roots of the polynomial eq. x^3-3x^2-5x-15=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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mathmate
  • mathmate
Are you familiar with Descarte's rule of signs?
mathmate
  • 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.
anonymous
  • anonymous
no ive neve used it

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anonymous
  • anonymous
never
mathmate
  • 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.
anonymous
  • anonymous
maybe a numerical method to find the roots?
mathmate
  • mathmate
I agree,... if the question had been correctly posted.
anonymous
  • anonymous
or graphing calculator?
KingGeorge
  • 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.
mathmate
  • mathmate
True, that is for getting an initial estimate.
mathmate
  • mathmate
@evy15 we're waiting anxiously your confirmation of the equation!! :)
anonymous
  • anonymous
agree... check that last term... should it really be -15 ???
anonymous
  • anonymous
yes the equation is correct
mathmate
  • 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).
anonymous
  • anonymous
`no its negative
mathmate
  • 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?
mathmate
  • 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?
anonymous
  • anonymous
@evy15 Is this homework? Are there certain methods you are supposed to be learning?
anonymous
  • anonymous
Once you find the 1st root, you can use synthetic division an the quadratic equation to find the other two.
anonymous
  • anonymous
is it -3
anonymous
  • anonymous
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.
KingGeorge
  • 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.
anonymous
  • anonymous
the thing is im completely confused because I missed a day in class and now idk how to do it
anonymous
  • anonymous
its typed in correctly
anonymous
  • anonymous
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 =/
KingGeorge
  • KingGeorge
I agree^^
anonymous
  • anonymous
and like others have mentioned, if only one of the signs is changed, it becomes an easy regular standard problem.
KingGeorge
  • KingGeorge
Unless, of course, you're learning about methods to approximate roots.
anonymous
  • anonymous
oh yeah. that could be the case. Newtons Method :)
anonymous
  • anonymous
its typed correctly
anonymous
  • anonymous
PLEASE HELP
anonymous
  • anonymous
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...
anonymous
  • anonymous
or graphing calc. or wolfram.
anonymous
  • anonymous
on calculator I got -15
anonymous
  • anonymous
If the problem as typed is correct, there is nothing we (or anyone) can do. Not without a calc or comupter, or something.
anonymous
  • anonymous
try to see if x=-15 is a root by plugging that back into the original equation... i don't think that's right.
anonymous
  • anonymous
wait... do you mean to find the y-intercept of \(\large y=x^3-3x^2-5x-15 \) ?? because -15 is the y-intercept...
anonymous
  • anonymous
if thats the actual problem....then lol.
anonymous
  • anonymous
ok thanks
anonymous
  • anonymous
ho boy...
mathmate
  • mathmate
Isn't the question: "Find the roots of the polynomial eq. x^3-3x^2-5x-15=0"
anonymous
  • anonymous
yes
mathmate
  • 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.

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