Zeroes - roots of polynomials, Algebra

We'll begin this section by defining just what a root or zero of a polynomial is.  We say that x = r is a root or zero of a polynomial, P ( x) , if P ( r )= 0 .  In other terms x= r is a root or zero of a polynomial if it is a solution to the equation P ( x)= 0 .

In the next couple of sections we will have to find all the zeroes for a given polynomial.  thus, before we get into that we eh to get some ideas out of the way about zeroes of polynomials that will help us in that procedure.

The procedure of finding the zeros of P ( x ) really amount to nothing more than solving out the equation P ( x )= 0 and already we know how to do that for second degree (quadratic) polynomials.  Hence, to help illustrate some of the ideas were going to be looking at let's get the zeroes of a couple of second degree polynomials.

Let's first determine the zeroes for P ( x)=x2+ 2x -15 .  To do this simply we solve out the following equation.

x2+ 2 x -15 =( x + 5)(x - 3)= 0  ⇒  x = -5, x = 3

Thus, this second degree polynomial has two zeroes or roots.

Now, let's determine the zeroes for P ( x)= x2 -14 x + 49 . 

That will mean solving,

x2 -14x + 49 =( x - 7 )2= 0  ⇒  x = 7

Hence, this second degree polynomial contains a single zero or root. Also, remember that while we first looked at these we called a root like this a double root.

We solved out each of these by first factoring the polynomial and then by using the zero factor property onto the factored form.  While we first looked at the zero factor property we saw that it said that if the product of any two terms was zero then one of the terms had to be zero to begin with.

The zero factor property can be extended to as several terms as we need.  In other terms, if we've got a product of n terms i.e. equal to zero, then at least one of them had to be zero to start off with.  Thus, if we could factor higher degree polynomials then we could solve these as well.

Posted Date: 4/8/2013 2:37:49 AM | Location : United States







Related Discussions:- Zeroes - roots of polynomials, Assignment Help, Ask Question on Zeroes - roots of polynomials, Get Answer, Expert's Help, Zeroes - roots of polynomials Discussions

Write discussion on Zeroes - roots of polynomials
Your posts are moderated
Related Questions
how to simplifie radicals

Find the zeros of the function by using the quadratic formula. Simplify your answer as much as possible. g(x)= 2x^2+4x-12

2(5+6csquared)-30divided by 3 c=2 d=4

2x^3+y+x+2x^2y

Give all solutions of the nonlinear system of equations including those with nonreal complex compents: xy=-20 3x+5y=5

i dont want the answer but how i shouuld find the answer plz :A rectangular display case houses a square pyramid. Both have the same square base measuring x inches on a side. The t

Hi I need help for the next 4weeks with my online math class I have included one assignment instruction below if you can help me please give me a quote I also have math labs that I

how many does a rhombus have


Mr.Carr is installing wall-to-wall carpeting in a room that measures 12 1/2ft. by 9ft. How much will it cost Mr. Carr if he purchases carpet priced at $26.00 per square yard?