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