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- Feb 14, 2012

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I have tried my very best to solve for $x$ in this problem, a quartic with a very large coefficient of $x^2$ but a small coefficient of $x^4$ and $x$ ,but ended up failing miserably...

I began to think it is a function that has no real roots because it just makes me feel better to think of it that way! But seriously though, I think it's a doable problem, but it's just that my ability to solve it is limited.

Could anyone show me the correct approach to crack it?

Thanks in advance.

Problem:

Find all real roots of the quartic $x^4-(2k + 1)x^2 -x + k^2+ k - 1 = 0$ correct to 4 decimal places, where $k= 10^{10}$.