Determine each real root of \[x^4-(2\cdot10^{10}+1)x^2-x+10^{20}+10^{10}-1=0\]correct to four decimal places.
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Tags: AMC, USA(J)MO, USAMO, quadratics, algebra unsolved, algebra, biquadratic
Dr Sonnhard Graubner
26.07.2011 22:17
hello, is $n$ the same as $N$ in your equation? Sonnhard.
Mrdavid445
26.07.2011 22:27
Dr Sonnhard Graubner wrote: hello, is $n$ the same as $N$ in your equation? Sonnhard. Correct
SMOJ
18.06.2014 16:36
This problem was not the original problem. The original problem was "Find all real roots of the quartic $x^4-(2N+1)x^2-x+N^2+N-1=0$ correct to 4 decimal places, where $N=10^{10}$"
utkarshgupta
19.06.2014 10:06
Just solve the equation in quadratic with $N$ as the variable. I think that should give you your answer.
namanrobin08
07.10.2024 18:14
utkarshgupta wrote: Just solve the equation in quadratic with $N$ as the variable. I think that should give you your answer. I *think* I am a little late in asking this, but what would we do after this? (10 years are not much I suppose)