Polynomial satisfy - rational root theorem, Algebra

Example: prove that the roots of the below given polynomial satisfy the rational root theorem.

P ( x ) = 12x3 - 41x2 - 38x + 40 = ( x - 4) (3x - 2) ( 4x +5)

Solution

From the factored form we can illustrates that the zeroes are,

                           x= 4 = 4/1         x= 2/3                x= - 5/4

Notice that we wrote the integer like a fraction to fit it into the theorem.  Also, along with the negative zero we can put the -ve onto the numerator or denominator.  It won't issue.

Thus, in according to the rational root theorem the numerators of these fractions (with or without the minus sign on the third zero) have to all be factors of 40 and the denominators have to all be factors of 12.

Here are various ways to factor 40 & 12.

40 =( 4) (10)               40 = ( 2) ( 20)      40 = (5) (8)         40 = ( -5) ( -8)

 

12 = (1) (12)              12 = (3) ( 4)                                12 = ( -3) ( -4)

From these we can illustrate that actually the numerators are all factors of 40 and the denominators are all factors of 12.  Also notice that, as illustrated, we can put the minus sign on the third zero on either the numerator or the denominator and still it will be a factor of the suitable number.

Posted Date: 4/8/2013 2:55:54 AM | Location : United States







Related Discussions:- Polynomial satisfy - rational root theorem, Assignment Help, Ask Question on Polynomial satisfy - rational root theorem, Get Answer, Expert's Help, Polynomial satisfy - rational root theorem Discussions

Write discussion on Polynomial satisfy - rational root theorem
Your posts are moderated
Related Questions
solve each equation for given variable 3ab-2bc=12;



what is 3.16 x 10^3= ?


In the last two sections of this chapter we desire to discuss solving equations & inequalities that have absolute values.  We will look at equations along with absolute value in th

Solve the system y = -x + 7 and y = -0.5(x - 3)^2 + 8

List the multiplicities of the zeroes of each of the following polynomials.              P ( x ) = 5x 5 - 20x 4 + 5x3 + 50x2 - 20x - 40 = 5 ( x + 1) 2 ( x - 2) 3 Solutio