The product of two of the four roots of the equation x⁴–18x³+Kx²+200x–1984=0 is –32. Find the value of K.

We are given that the product of the two roots are -32, so I started looking at the different possibilities. -8 * 4, 8*-4, -16 * 2, 16 * -2, -32 * 1, and 32 * -1.

First I plugged x=8 into the equation and got that

64K=-5504.

So K=-86.

Then I checked its pair, x=-4.  Plugging this in I got

16K=-1376.

So K=-86.

Since both x=8 and x=-4 give the same K value, K=-86 is the solution.

Posted by Becky on 2006-05-17 14:57:15