Answered: Find an nth-degree polynomial function…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.CR: Chapter Review

Problem 61E

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Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. n=3; 3 and 4 i are zeros; f(1)=34

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$w e h a v e g i v e n n = 3 a n d 3 a n d 4 i a r e t h e r o o t s o f p o l y n o m i a l a n d f (1) = 34 i f w e t a k e p o l y n o m i a l w i t h r e a l c o - e f f i c i e n t t h e n o n e r o o t i s i m a g i n a r y t h e n o t h e r r o o t i s i t s c o n j u g a t e t h a t i s r o o t s o f t h e p o l y n o m i a l o f t h r e e d e g r e e i s (x - 4 i) (x + 4 i) (x - 3) = 0 \Rightarrow (x^{2} + 16) (x - 3) = 0 \Rightarrow x^{3} - 3 x^{2} + 16 x - 48 = 0 n o w w e t a k e - 1 a s c o m m o n w e g e t, \Rightarrow - x^{3} + 3 x^{2} - 16 x + 48 = 0 i t s s a t i s f y f (1) = 34$

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