Equations and Factoring

Date: 2/5/96 at 12:20:5
From: Anonymous
Subject: Polynomial equations/inequalities

I don't understand how to figure the problems:

Solve. Identify all double roots.
   2(r squared + 1)=5r 
   2(r squared + 1)-5r=0
   2r squared + 2 - 5r=0
   2r squared - 5r +2=0
   (2r   )(1r   )

What have I done wrong and what do I need to do to finish it?

Find and graph the solution set of each inequality.
   4y squared _> 36        _> is greater than/equal to 
   4y squared - 36 _> 0    

What next?

Date: 7/1/96 at 20:36:35
From: Doctor Paul
Subject: Re: Polynomial equations/inequalities

You're very close to finishing the problem.  The final part is 
factoring.

Here's how to do it:

(2r-1)(r-2)
Using FOIL, multiply it out and you get:
r2^2 - 4r - r + 2
that simiplifies to what you had originally.

Now let's set it equal to zero and get answers for values of r 
that satisfy your conditions.  

You have:
(2r-1)(r-2) = 0

The only way the entire equation can be equal to zero is if 
either of the parts (2r-1 or r-2) is equal to zero.  So set each of 
those equal to zero and solve..

2r-1 = 0         r-2 = 0
2r = 1           r = 2
r = 1/2

so r = 1/2 and r = 2 are the solutions to your quadratic.

Feel free to ask Dr. Math more questions!

-Doctor Paul,  The Math Forum