SOLUTION: Can you help me tonight with this problem? Find all positive values for k for which each of the following can be factored. x^2 + x - k Thanks for your help.

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Question 95598This question is from textbook Beginning Algebra
: Can you help me tonight with this problem?
Find all positive values for k for which each of the following can be factored.
x^2 + x - k
Thanks for your help. This question is from textbook Beginning Algebra

Answer by stanbon(75887) About Me  (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.
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That depends on what restrictions there are on the factors.
Actually every quadratic can be factored; the quadratic
equation quarantees that.
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I'm going to assume your question means "factor in the Real
Number System".
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In that case b^2-4ac must be greater than or equal to zero:
x^2 + x - k
b^2-4ac = 1^2-4*1*-k = 1+4k must be >=0
1-4k>=0
4k<=1
k<=1/4
As long as k<=1/4 the quadratic will have Real Number
roots and will have factors with Real Numbers.
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That is the best answer I can come up with. If you have
more information regarding the problem, post it again with
the additional information.
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Cheers,
Stan H.