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

- anonymous

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

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- mathmate

Are you familiar with Descarte's rule of signs?

- 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

no ive neve used it

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## More answers

- anonymous

never

- 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

maybe a numerical method to find the roots?

- mathmate

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

- anonymous

or graphing calculator?

- 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

True, that is for getting an initial estimate.

- mathmate

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

- anonymous

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

- anonymous

yes the equation is correct

- 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

`no its negative

- 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

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

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

- anonymous

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

- anonymous

is it -3

- 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

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

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

- anonymous

its typed in correctly

- 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

I agree^^

- anonymous

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

- KingGeorge

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

- anonymous

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

- anonymous

its typed correctly

- anonymous

PLEASE HELP

- 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

or graphing calc. or wolfram.

- anonymous

on calculator I got -15

- 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

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

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

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

- anonymous

ok thanks

- anonymous

ho boy...

- mathmate

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

- anonymous

yes

- 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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