Question 983280: X^3-7x^2-6x+3=0
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! Factorize? Best try synthetic division, as if for checking possible roots. If remainder of 0, then value checked is a root of the equation. When one root found, the two other roots will come from handling the result quadratic expression (the quotient from the first root found).
-1 | 1 -7 -6 3
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| -1 6 0
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1 -6 0 3
+1 | 1 -7 -6 3
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| 1 -6 -12
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1 -6 -12 -9
-3 | 1 -7 -6 3
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| -3 30 -72
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1 -10 24 -69
+3 | 1 -7 -6 3
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| 3 -12 -54
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1 -4 -18 -51
All the possible RATIONAL roots failed to give remainder of 0.
Next method should be some numerical root finding approximation. You might also use a graphing tool.
If you are in a hurry (no longer likely), or want to recheck your results, or you believe some roots are complex or irrational, you might try using this:
http://xrjunque.nom.es/rootfinder.aspx
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