Question

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

Answer 1

Are you familiar with Descarte's rule of signs?

Answer 2

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

Answer 3

no ive neve used it

Answer 4

never

Answer 5

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.

Answer 6

maybe a numerical method to find the roots?

Answer 7

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

Answer 8

or graphing calculator?

Answer 9

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.

Answer 10

True, that is for getting an initial estimate.

Answer 11

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

Answer 12

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

Answer 13

yes the equation is correct

Answer 14

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).

Answer 15

`no its negative

Answer 16

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?

Answer 17

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?

Answer 18

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

Answer 19

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

Answer 20

is it -3

Answer 21

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.

Answer 22

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.

Answer 23

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

Answer 24

its typed in correctly

Answer 25

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 =/

Answer 26

I agree^^

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

its typed correctly

Answer 31

PLEASE HELP

Answer 32

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...

Answer 33

or graphing calc. or wolfram.

Answer 34

on calculator I got -15

Answer 35

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

Answer 36

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

Answer 37

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

Answer 38

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

Answer 39

ok thanks

Answer 40

ho boy...

Answer 41

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

Answer 42

yes

Answer 43

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.