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Homework Help: Solve using quadratic formula?

  1. Jan 18, 2012 #1
    1. The problem statement, all variables and given/known data

    Hey guys, recently, I struggled to solve this equation.
    I need to find θ1 and θ2 by using this system of equations:


    After letting θ2=β/θ1, I plugged this into the first equation. I got:


    At this point I get a very unsexy θ1 result by using quadratic solution.

    Need you help!

    P.S. This way, I get 4 solutions overall, but my professor is saying that there should only be 2 solutions.
  2. jcsd
  3. Jan 18, 2012 #2


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    What you've done so far is just fine. And I don't think the answer is going to pretty no matter how you do it.
  4. Jan 19, 2012 #3

    Ray Vickson

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    How did you get 4 solutions? Could you show us? The point is that you must have made an error, and we cannot help until we know what you did.

  5. Jan 19, 2012 #4


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    If you look at your equations they are symmetric between θ1 and θ2. You could say there is no difference between θ1 and θ2. Or, do what you did to get a quadratic equation for θ1 but do it to get an equation for θ2 instead - you find you have got exactly the same equation for θ2 as you got for θ1.

    You haven't really got two quadratic equations, you've got one.
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