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I'm having trouble with the following factoring problem, but I'm not even sure if a function like this can be factored to begin with. This is actually a small step in another problem that I'm working on, but this function needs to be factored:

$f(x) = x - \lambda x^2 -1$ where $0 < \lambda < \frac{1}{4}$

So in general can functions with parameters like this be factored, and if so, is there a general procedure for getting it done?

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up vote 2 down vote accepted

The discriminant of the quadratic function $f$ is $$\Delta= 1-4\lambda>0$$ then $f$ has two distinct real roots $x_1=\frac{1-\sqrt{1-4\lambda}}{2}$ and $x_2=\frac{1+\sqrt{1-4\lambda}}{2}$ hence we find $$f(x)=-\lambda(x-x_1)(x-x_2)$$

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this makes sense, thanks! – Benzne_O Apr 12 '13 at 13:01
You're welcome. – user63181 Apr 12 '13 at 13:08

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