Equations and FactoringDate: 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 |
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