Can someone pls help me on this question. x^2+x-k. Find all positive values for k than can be factored?

Question: I am asuming that x is 1?

Answer: Suppose it factors with roots a and b. Then: x^2+x-k = (x-a)(x-b) = x^2 -(a + b)x + ab So doing a variable comparisson gives: 1 = -(a+b) OR -1 = a+b -k = ab So it seems that there are a lot of answers: a = 1 b = -2 works a = 0 b = -1 works --- Below these will be reflections of those above: a = -1 b = 0 works a = -2 b = 1 works a = -3 b = 2 works a = -4 b = 3 etc. So you will get k values of: 0,2,6,12, 20,... and so on (note: 0 is not positive so it isnt a solution) You have a lot of k values I hope this helps!

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