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Bug in NSolve?


The Mathematica book says in section 2.9.5:

"NSolve will always give you the complete set of numerical solutions to any
polynomial equation in one variable."

However,  Mathematica version 4.1.2  on a Pentium III gives this result:

NSolve[4877361379 x^2 -9754525226 x + 4877163849==0,x,20]

{{ x---> 0.9999797501 }}

On the other hand, 

NSolve[4877361379 x^2 -9754525226 x + 4877163849==0,x,10]

gives:

{{ x ---> 0.99998 } , { x---> 0.99998 } }

Machine precision works, but arbitrary precision doesn't?

At least now we get two roots; the correct solution is given by:

N[Solve[4877361379 x^2 -9754525226 x + 4877163849==0,x ] ,10]

which is:

{{ x ---> 0.99998 - 2.89955 x 10^-10 i },{ x---> 0.99998 + 2.89955 x 10^-10i }}

Does anybody know what's going on here?




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