Solve : x^101 + x^52 + x^50 + x^2 - 1 = 0

TheOAP

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Nov 5, 2017
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Solve : x^101 + x^52 + x^50 + x^2 - 1 = 0

By program :

* No Rational roots found *
Irrational/repeating root(s) :
between
-0.944787384 and -0.944787383
0.943986614 and 0.943986615


Try it on your graphing program...
Pete
 
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By program :

* No Rational roots found *
Irrational/repeating root(s) :
between
-0.944787384 and -0.944787383
0.943986614 and 0.943986615

Did you notice that the [original problem] was not to find zeros (solve an equation), but to factor the polynomial, which you haven't done.

On the other hand, what Wolfram Alpha did when told to solve the equation was not to factor it as a product of linear and quadratic factors, which is what we usually mean by "factor fully". It just did what others have suggested.

If you ask it to factor, rather than to solve, it is clear that full factorization can't have been intended: http://www.wolframalpha.com/input/?i=factor+X^101+++X^52+++X^50+++X^2+-+1 .
 
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