Posted by **Scott** on Monday, July 23, 2007 at 10:05pm.

Find all positive values for k for which each of the following can be factored.

X^2-x-k

(Your answer seems to be the same as the other problem x^2+x-k )

Is this correct too?

Consider your equation to be in the form ax^2 + bx = c = 0. It can be factored (that is, have real answers for x) if the term b^2 - 4ac is positive or zero. In your case,

b^2 - 4ac = 1 + 4k, so 1+4k >or= 0

k >or= -1/4

If k = -1/4, you have the special case

(x-1/2)^2 = 0, with only one root, x = 1/2

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