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A Biquadratic Polynomial Problem (Posted on 2006-11-20) Difficulty: 3 of 5
Determine analytically if two of the roots of x4+12x-5=0 add up to 2.

See The Solution Submitted by K Sengupta    
Rating: 3.0000 (2 votes)

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Solution Solution | Comment 1 of 3

 x^4 + 12x - 5
   = (x^2 + 2x - 1)*(x^2 - 2x + 5)
   = [x + 1 - sqrt(2)]*[x + 1 + sqrt(2)]*
     [x - 1 - 2i]*[x - 1 + 2i]
Thus, the roots are
   -1 - sqrt(2),
   -1 + sqrt(2),
    1 - 2i, and
    1 + 2i
The sum of the last two is 2.

  Posted by Bractals on 2006-11-20 15:40:33
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