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

- katieb

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- 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

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## 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.

Looking for something else?

Not the answer you are looking for? Search for more explanations.