5.5 Theorems about Roots of Polynomial Equations P312-315.

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Presentation transcript:

5.5 Theorems about Roots of Polynomial Equations P

So this means that the POSSIBLE RATIONAL ROOTS have the form Factor of constant term Factor of leading coefficient

Ex) What are the rational roots of ? Steps…. Find the possible rational roots. Test the possible rational roots to find a root. Factor polynomial by using synthetic division. Use factored polynomial to find other roots.

Ex) What are the rational roots of ?

This means that Irrational roots come in conjugate pairs Imaginary roots come in conjugate pairs

Ex) A quartic polynomial P(x) has rational coefficients. If and are roots of P(x)=0, what are the other roots?

Ex) What is a third degree polynomial function y = P(x) with rational coefficients so that P(x)=0 has the roots and ?

Ex) What does Descarte’s Rule of Signs tell you about the real roots of ?