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August 26th, 2011, 07:00 AM  #1 
Newbie Joined: Aug 2011 Posts: 3 Thanks: 0  Factor this second degree polynomial
I hit an impasse when trying to isolate x from the following equation (dual second degree polynomial?): (1.5*x)^2+x^2=3.5^2 What rules do I apply, in order to factor (1.5*x)^2+x^2 into one square expression so that I may treat it as a classic second degree polynomial (ax^2 + bx + c = 0)? Using numberempire.com I am able to come up with concrete answers, the above resolves to 7/sqrt(13). However, I am a bit embarrassed not being able to remember my algebra and would love to know just how numberempire.com arrives at this answer. Could a kind math soul help out? 
August 26th, 2011, 07:08 AM  #2 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: Factor this second degree polynomial [color=#000000]I don't see why it is so difficult, .[/color] 
August 26th, 2011, 07:23 AM  #3 
Newbie Joined: Aug 2011 Posts: 3 Thanks: 0  Re: Factor this second degree polynomial
Interesting... thanks ZardoZ! I was hoping to be able to rewrite it so I could plug it into a spreadsheet, letting 1.5 (a) and 3.5 (d) being variables... it doesn't look like that is easily done though: (a*x)^2+x^2=d^2 All I really want to arrive at, is calculating the area of a rectangle using only the ratio of the sides and the diagonal (as in, calculating the surface area of monitor, knowing only the physical resolution and diagonal size, say 1024x768 and 19"). Can this be done? 
August 26th, 2011, 10:12 AM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Factor this second degree polynomial
You may solve for x: For finding the area of a rectangle armed only with the diagonal measurement d and the aspect ratio a (ratio of width x to height y), we may use: (1) (2) From (1), we find and substituting into (2) we get: Now, take x = ay, and multiply both sides by y: Since the area A of the rectangle is xy, we have: 
August 26th, 2011, 10:29 AM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond  Re: Factor this second degree polynomial This should give a fair approximation of the viewable area of the monitor  horizontal scaling may be a little different than its vertical counterpart. The link below may help. http://en.wikipedia.org/wiki/Pixel_dens ... onitor_PPI 
August 30th, 2011, 11:36 AM  #6 
Newbie Joined: Aug 2011 Posts: 3 Thanks: 0  Re: Factor this second degree polynomial
Thanks a lot guys! 

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