Here's the question you clicked on:
evy15
Find the roots of the polynomial eq. x^3-3x^2-5x-15=0
Are you familiar with Descarte's rule of signs?
Using Descartes rule of signs, we know that there is one positive real root, and either two negative real roots, or two complex roots.
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.
maybe a numerical method to find the roots?
I agree,... if the question had been correctly posted.
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.
True, that is for getting an initial estimate.
@evy15 we're waiting anxiously your confirmation of the equation!! :)
agree... check that last term... should it really be -15 ???
yes the equation is correct
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).
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?
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?
@evy15 Is this homework? Are there certain methods you are supposed to be learning?
Once you find the 1st root, you can use synthetic division an the quadratic equation to find the other two.
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.
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.
the thing is im completely confused because I missed a day in class and now idk how to do it
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 =/
and like others have mentioned, if only one of the signs is changed, it becomes an easy regular standard problem.
Unless, of course, you're learning about methods to approximate roots.
oh yeah. that could be the case. Newtons Method :)
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...
or graphing calc. or wolfram.
If the problem as typed is correct, there is nothing we (or anyone) can do. Not without a calc or comupter, or something.
try to see if x=-15 is a root by plugging that back into the original equation... i don't think that's right.
wait... do you mean to find the y-intercept of \(\large y=x^3-3x^2-5x-15 \) ?? because -15 is the y-intercept...
if thats the actual problem....then lol.
Isn't the question: "Find the roots of the polynomial eq. x^3-3x^2-5x-15=0"
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.