Math Problem Statement
- Find all of the zeros and multiplicities of the function 𝑓𝑓(𝑥𝑥) = 𝑥𝑥 5 + 𝑥𝑥 4 − 19𝑥𝑥 3 + 17𝑥𝑥 2 + 48𝑥𝑥 − 60. Begin by finding the possible rational zeros by applying the Rational Zero Theorem 𝑝𝑝 𝑞𝑞. Then graph the function on your calculator and make predictions of rational zeros from the graph. Check your predictions using synthetic division, and finally solve the remaining quadratic to find all the zeros. Show all work.
Solution
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Math Problem Analysis
Mathematical Concepts
Polynomial Functions
Rational Zero Theorem
Synthetic Division
Quadratic Equations
Formulas
Rational Zero Theorem: Possible rational zeros = p/q where p is a factor of the constant term, q is a factor of the leading coefficient
Synthetic Division Process
Theorems
Rational Zero Theorem
Suitable Grade Level
Grades 10-12
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