According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 5x3 – 7x + 11?
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The Rational Root Theorem tells us that if there is a rational root p/q (in lowest terms) of this polynomial, then:
p is a factor of 11 and q is a factor of 5.
The factors of 11 are -11, -1, 1, 11.
The factors of 5 are -5, 1, 1, 5.
So by the Rational Root Theorem, if there are rational roots at all, then they must be among the eight numbers
-11/5, -11, -1/5, -1, 1, 1/5, 11, 11/5
Anonymous:
Incidentally, testing these one at a time, none of them turns out to be a root. So we can then say further that f(x) has no rational roots at all.
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