Question 97701: Find all positive values for k for which each of the following can be factored.
x^2+x-k
I've tried everything and it just isn't making sense to me since there are no numbers to factor.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find all positive values for k for which each of the following can be factored.
x^2+x-k
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If you make the assumption that the factoring is limited to the
Real Number System, then b^2-4ac must be greater than or equal
to zero.
Your Problem:
a=1, b=1, c=k
b^2-4ac = 1-4k>=0
4k<=1`
k<=(1/4)
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As long as k<=(1/4) the quadratic will be factorable
in the Real Number System.
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Cheers,
Stan H.
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