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Question 1046255: Solving the equation in the real number system. x^4-3x^3+5x^2-x-10=0
Answer by josgarithmetic(39613)   (Show Source):
You can put this solution on YOUR website! Possible roots to try using synthetic division are -10,-5,-2,-1,1,2,5,10.
-1 | 1 -3 5 -1 -10
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| -1 4 -9 10
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1 -4 9 -10 0
2 | 1 -4 9 -10
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| 2 -4 10
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1 -2 5 0
Both -1 and +2 are roots for the degree four expression. The factorization of the equation would be
 and you would like to find any other REAL roots, because that is what your
question specifies.
The discriminant of the found quadratic factor is  , negative, therefore  has NO REAL ROOT.
The solution for the original given equation is therefore  .
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