Find the value of c for?

A value c for which the given equation has 2 distinct negative roots.

$$x^4 + 2cx^2 + 2cx + 1 + x^2 = 0$$

I solved it up to here, what does this imply ?

$$\sqrt{ 1+c^2 } > 2 - c$$

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Could you should how you arrived at this inequality? It's not correct. –  icurays1 Dec 16 '12 at 17:15

If we square both sides, we get $1+c^2>(2-c)^2=4-4c+c^2$, which after cancelling $c^2$ and rearranging tells us that
$$c>\frac{3}{4}$$
This is assuming your work up to this point is ok, which I'm not sure it is - if $c=1$, your equation has no real roots.