Rational Zeros Calculator
MathFind all possible and actual rational zeros of a degree-4 polynomial using the rational root theorem.
Possible Rational Zeros
Every candidate value the rational root theorem allows, plus-or-minus each factor of the constant term over each factor of the leading coefficient.
Actual Rational Zeros
-2, 0.5
Which of the possible candidates are actually zeros of the polynomial, confirmed by plugging each one in.
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Odeh Ahwal0people find this calculator helpful
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Frequently Asked Questions
What is the rational root theorem?
It says that if a polynomial with integer coefficients has a rational zero p/q (in lowest terms), then p must be a factor of the constant term and q must be a factor of the leading coefficient. This narrows an infinite search down to a short list of candidates.
Why are there so many candidates but few actual zeros?
The rational root theorem only narrows down the possibilities, it does not guarantee any of them are real zeros. Each candidate still has to be tested by plugging it into the polynomial and checking whether the result is zero.
What if the polynomial has no rational zeros at all?
That is common. Many polynomials have only irrational or complex roots, in which case none of the rational root theorem's candidates will actually work, even though the theorem still correctly lists every candidate worth checking.
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