
Linear Algebra Linear Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: CA Posts: 1,301 Thanks: 664 
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: 17,729 Thanks: 1360 
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  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
quadratic equation roots  bongantedd  Algebra  3  February 22nd, 2014 07:10 AM 
Sum & Product of the Roots of a Quadratic Equation  bilano99  Algebra  5  April 21st, 2013 06:08 PM 
Quadratic equation nature of roots  sachinrajsharma  Algebra  7  March 21st, 2013 02:54 PM 
Quadratic Equation Ratio of roots  sachinrajsharma  Algebra  1  February 20th, 2013 08:11 AM 
Sum & Product of the Roots of a Quadratic Equation  bilano99  Algebra  4  June 18th, 2012 09:26 AM 