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Find 'K' (Posted on 2006-05-15) Difficulty: 3 of 5
The product of two of the four roots of the equation x418x3+Kx2+200x1984=0 is 32. Find the value of K.

No Solution Yet Submitted by Ravi Raja    
Rating: 3.0000 (1 votes)

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Solution Solution | Comment 2 of 3 |

From the givens, we have
  x^4 - 18x^3 + K x^2 + 200 x - 1984 =
  (x^2 + A x - 32)(x^2 + B x + 62) =
  x^4 + (A + B)x^3 + (AB + 30)x^2 + 2(31A - 16B)x - 1984
Setting the coefficients equal gives
  A + B = -18
  AB + 30 = K
  31A - 16B = 100
Solving these gives
  A = -4
  B = -14
  K = 86
 

  Posted by Bractals on 2006-05-16 18:18:26
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