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 August 23rd, 2016, 08:29 AM #1 Newbie   Joined: Aug 2016 From: india Posts: 2 Thanks: 0 how to find the roots of the following quadratic equation? x^2+[((a^2))/((a^2+b^2))+((a^2+b^2))/(a^2)]x+1=0 What the roots of the above equation? Last edited by skipjack; August 23rd, 2016 at 09:00 AM. August 23rd, 2016, 09:04 AM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,468 Thanks: 1342 Just use the quadratic formula $a=1$ $b=\dfrac{a^2}{a^2+b^2}+\dfrac{a^2+b^2}{a^2}$ $c=1$ It will be a mess, true. Last edited by skipjack; August 23rd, 2016 at 09:18 AM. August 23rd, 2016, 09:17 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,757 Thanks: 2138 The equation is cluttered with redundant parentheses. It's of the type $\displaystyle x^2 + (p + 1/p)x + 1 = 0$, which factorizes as $\displaystyle (x + p)(x + 1/p) = 0$. $\displaystyle x^2 + \left(\frac{a^2}{a^2 + b^2} + \frac{a^2 + b^2}{a^2}\right)x + 1 = \left(x + \frac{a^2}{a^2 + b^2}\right)\left(x + \frac{a^2 + b^2}{a^2}\right) = 0$ is easy to solve. August 24th, 2016, 04:36 AM #4 Newbie   Joined: Aug 2016 From: india Posts: 2 Thanks: 0 thanks Tags equation, find, quadratic, roots Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post bongantedd Algebra 3 February 22nd, 2014 07:10 AM bilano99 Algebra 5 April 21st, 2013 06:08 PM sachinrajsharma Algebra 7 March 21st, 2013 02:54 PM sachinrajsharma Algebra 1 February 20th, 2013 08:11 AM bilano99 Algebra 4 June 18th, 2012 09:26 AM

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