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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: 2,403 Thanks: 1306 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: 20,464 Thanks: 2038 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

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