section 5.5 theorems about roots of polynomial equations
TRANSCRIPT
Section 5.5
Theorems about Roots of Polynomial Equations
Rational Root Theorem
• All possible rational roots are in the list of:factors of the constantfactors of the L.C.
Example: Any rational root for will be in the list:
3 22x x 2x 5 0
Find all the roots of: ( ) 3 2f x 15x 32x 3x 2
What are the rational roots of:3 22x x 7x 6 0
Conjugate Root Theorem
• A polynomial with rational coefficients will always have complex roots that are complex conjugate pairs. This is also true of irrational roots but only if the coefficients are rational.
• For example, if 2 - 3i is a root then 2 + 3i is also a root. If √5 is a root then -√5 is also a root.
If are roots, what are two other roots?
2 and 1 i
What is a third-degree polynomial function with rational coefficients
that has roots -4 and 2i?