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August 23rd, 2016, 09:29 AM   #1
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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 10:00 AM.
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August 23rd, 2016, 10:04 AM   #2
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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 10:18 AM.
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August 23rd, 2016, 10:17 AM   #3
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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.
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August 24th, 2016, 05:36 AM   #4
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