Descartes' Rule of Signs Calculator
MathFind the possible number of positive and negative real roots of a degree-5 polynomial using Descartes' rule of signs.
Max Possible Positive Real Roots
The number of sign changes in the coefficients, an upper bound on positive real roots (the actual count is this number or less, by an even number).
Max Possible Negative Real Roots
3
The number of sign changes after substituting -x for x, an upper bound on negative real roots (the actual count is this number or less, by an even number).
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Odeh Ahwal0people find this calculator helpful
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Frequently Asked Questions
What is Descartes' rule of signs?
It is a rule that estimates the number of positive and negative real roots of a polynomial just by counting sign changes between consecutive coefficients, without actually solving the polynomial.
Why is the actual root count "this number or less by an even number"?
Complex roots of a real-coefficient polynomial always come in pairs, so any pair of possible real roots not realized shows up instead as one pair of complex roots. This always reduces the real root count by an even amount from the sign-change upper bound.
Why does finding negative roots involve substituting -x?
Substituting -x for x flips the sign of every odd-power term, turning the question "how many negative roots does p(x) have" into "how many positive roots does p(-x) have," which the same sign-counting rule can then answer.
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