Question 97701
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.