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Finding Zeros of Polynomials


Date: 11/13/2001 at 21:23:39
From: Yazmin Alvarez
Subject: Finding zeros of polynomials

Can you explain how to find the zeros of polynomials?
Also, can you give me an example of an application?


Date: 11/15/2001 at 10:55:06
From: Doctor Code
Subject: Re: Finding zeros of polynomials

Hi Yazmin,

There are different ways to find zeros.  The easiest is when the 
polynomial is factorable:

     x^2 + 5x + 6 = 0

   (x + 2)(x + 3) = 0

The zeros are the values for x that make the value of the polynomial 
equal to zero. In the above example, it's when x = -2 and when x = -3.

If the polynomials aren't factorable, you have to use another method 
such as Newton's Method, which you can find more information on in the 
Dr. Math archives:

   Finding Roots of Polynomials with Complex Numbers
   http://mathforum.org/dr.math/problems/ed.09.27.01.html   

One example from my field is a robot that has a hand, and is trying to
balance a broom. The question is, if the robot sees the broom tip a 
certain amount, how much force should the robot exert in order to keep 
the broom from falling? If the robot pushes too hard or too softly, 
the broom will fall over. One way to obtain the optimal force gains is 
to solve a simplified equation of motion of the broom. This equation 
is a quadratic polynomial, and getting the zeros of this polynomial 
will give you the force gains you need. You're probably thinking, who 
cares if a robot can balance a broom? But it turns out that nearly all 
robots need these sorts of techniques in order to move.

Write back if you need more help.

- Doctor Code, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Polynomials

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