Question 923140: Show that x = 1 is the only rational root for the polynomial f(x) = x^3 - 5x^2 +5x - 1.
Answer by josgarithmetic(39625)   (Show Source):
You can put this solution on YOUR website! Test 1 as a possible root of f(x) using synthetic division. Remainder 0 means root; otherwise, not root. Using Rational Roots Theorem, 1 is the ONLY possible root.
________1____|_____1_____ -5_______ 5________ -1
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_____________|____________1________-4__________1
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__________________1______-4_________1_________0
1 is a root of f(x), and it is the only rational root.
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