 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Find 'K' (Posted on 2006-05-15) The product of two of the four roots of the equation x4–18x3+Kx2+200x–1984=0 is –32. Find the value of K.

 No Solution Yet Submitted by Ravi Raja Rating: 3.0000 (1 votes) Comments: ( Back to comment list | You must be logged in to post comments.) 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 Please log in:
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