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Quadratic Equation

  1. Aug 8, 2007 #1

    How to find the equation if one root of a quadratic equation is 1 + 3i.


  2. jcsd
  3. Aug 8, 2007 #2

    Gib Z

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    Does the equation has real co efficients? If it does, the other root is the complex conjugate of that root. If not, and you have the co efficients which I dont think you do, then just set (x - your root) as a factor and divide. If you don't know any of that information, no way to tell.
    Last edited: Aug 8, 2007
  4. Aug 8, 2007 #3


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    Your "find the equation" implies that there is only one such equation. There isn't. If a quadratic equation has x0 and x1 as roots, then it must be of the form a(x-x0)(x- x1)= 0 where a can be any number.

    You know that one root is 1+ 3i. As Gib Z said, if your equation must have real coefficients, then the other root must be its complex conjugate 1- 3i so any equation of the form a(x- 1- 3i)(x- 1+ 3i)= 0 will work. If you do not require real coefficients, choose any complex number at all for the second root!
    Last edited: Aug 8, 2007
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