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get the real part of the problem (Posted on 2016-10-16) Difficulty: 3 of 5
x^8 - x^4 - 240 = 0

Consider all of the (possibly complex) roots to this equation. How many of them have a positive real part?

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution solution Comment 1 of 1
Define y = x^4

y^2 - y - 240 = 0

y = (1 +/- sqrt(1+960)) / 2 = -15 or 16


x^4 = 16 has roots of 2, -2, 2i and -2i, only one of which has a positive real part.

x^4 = - 15 has roots 15^(1/4)/sqrt(2) times choice of:
                               1+i, -1+i, -1-i and 1-i
        Two of these have positive real parts.
        
All together the equation has 3 roots with positive real parts, 3 with negative real parts and 2 with real part of zero.        

  Posted by Charlie on 2016-10-16 11:13:54
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