How do you find the roots/zeros of polynomials, with just the equation?

Question

How do you find the roots of polynomial equations with highest powers of either 3 or 4. Step by step directions would helike please.

 

Well, i have tried those methods. I still cant find an answer. The problems include:
x^4-3x^3+2x^2-7x-11
3sin(2x)-4x+1 (from -2pi to 2pi)
x^4-8x^2+5
x^3+3x^2-10x-1
100x^3-203x^2+103x-1

Answer 1

General steps:

1. Use a bunch of tricks from precalculus (Descartes' rule of signs, rational root theorem, etc) to find just one root to start.

 

2. Once you know one root, you can figure out its associated factor (for example, if a root is x=3 then the corresponding factor of the original polynomial is x-3). Use synthetic division or polynomial long division to divide out that found factor. This will reduce the degree of the polynomial by one.

 

3. See if you can now factor the resulting polynomial. If you can, you're finished. Otherwise go back to step one and hunt for the next root. Repeat the procedure until you've reduced the polynomial down to its basics.

Answer 2

Using the Rational Root Theorem, at least the first, third, fourth, and fifth expressions have no rational roots.  So, factoring won't help.  You could use an approximation method (such as Newton's Method), or you could use a graphical approach on a graphing calculator to approximate the real roots.  

 

Mark M. Bayport, NY

Answer 3

If you want help in completing your
1 Assignments
2 Homework
3 Online courses
4 Online Exams
5 Classroom exams

In subjects
1 Finance
2 Statistics
3 Economics
4 Accounting
5 Operations Research
6 Econometric
7 Investments
8 Mathematics
9 Physics
10 Chemistry
11 Probability
12 Business
13 Project Management
14 C programming
15 C++ Programming

Work related to
Minitab
Excel
SPSS
R language

If you have work related to other subjects, I have a bunch of tutors for other subjects at very low prices.

If you wish for live tutoring. I have a separate platform for that at rate 10 dollars per hour.

Perks
1 you can pay me after getting your work done.
2 My fees will be very less as compared to Wyzant and other tutoring sites.

You can contact me through

Facebook search
Wei-Chyung Wang

Mail Id (Gmail account)
ijddjebdyxtvbd

Kik messenger

imessage

You can send a message on Wyzant with your details

1 Your name
2 Subject
3 Work details
4 Contact number
5 Mail id

I am running workhelp site since 10 years. I have worked as a professor for 10 years and now with my team working to help students across the globe in their studies. We are working at other sites like chegg tutors as registered tutors.

Payment will be through Paypal.

Answer 4

Without a specific equation specific steps are not possible.

Some concepts that are helpful:

Rational Root Theorem

Des Cartes Rule of Signs

Synthetic Division/Substitution

 

Answer 5

One thing is missing from Mark's answer:

 

You must set the polynomial equal to zero.  For example, you have an equation such as

 

ax² + bx = c

 

 

You need to make one side of the equation equal to zero.  To do so, simplify subtract c on both sides of the equation.

 

ax² + bx - c = 0

 

 

Now you can use the following methods Mark mentioned.