Question

Using complete sentences, explain how the outcome of the Rational Root Theorem and Descartes’ Rule of Signs differ from one another.
Help me pretty please:)

Answer 1

The Rational Root Theorem gives information about the number of rational roots in a polynomial.

Descartes' Rule of Signs gives the information about the number of positive or negative roots in a polynomial. The roots may or may not be rational.

For example, if p(x) = x^2 + 1, the rational root test tells us that the only rational roots (if they exist) will be -1, and 1.

According to the rule of signs, there are no positive roots as there are no sign changes for p(x)), and there are no negative roots also as there are no sign changes for p(-x), which equals p(x) in this case
We see that the two tests can yield different results.

Answer 2

Thank you<3

Answer 3

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