SOLUTION: Find all the positive values for k for which each of the following can factored. x^2+x-k. please explain to me how to solve this problem and thank you in advance.

Question 101252: Find all the positive values for k for which each of the following can factored.

x^2+x-k.

please explain to me how to solve this problem and thank you in advance.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find all the positive values for k for which each of the following can factored.
x^2+x-k.
-------------
I will assume this means "factored in the Real Number System".
You have a quadratic with a=1,b=1,c=-k
The discriminant is b^2-4ac
The quadratic has Real Number roots (and therefore Real Number
factors) if b^2-4ac>=0
-------
So 1^2-4*1*(-k)>=0
1+4k>=0
4k<=1
k<=1/4
-------------
The quadratic will have Real Number factors if k<=1/4
==================
Cheers,
Stan H.
RELATED QUESTIONS
Find all the positive values for k for which each of the following can be factored... (answered by stanbon)

find all positive values for k for which each of the following can be factored.... (answered by Edwin McCravy)

Find all positive values for k for which each of the following can be factored. x^2 + (answered by Nate,ptaylor)

Find all positive values for k for which each of the following can be factored,... (answered by checkley71)

Find all positive values for k for which each of the following can be factored.... (answered by checkley71)

HELP PLEASE...Find all positive values for k for which each of the following can be... (answered by scott8148)

How do I do this? Find all positive values for k for which each of the following can be (answered by stanbon)

I need to find all of the positive values for k for which each of the following can be... (answered by stanbon)

find all positive values for k for which each of the following can be factored... (answered by checkley71)