Precalculus #1 - Questions and Answers | Answer Key - Edubirdie

University:
University of Michigan
Course:
MATH 116 | Calculus II
Academic year:

2024
Views:

391

Pages:

1
Author:

banenetta0l

Question 1 𝑛 = 4 ; 𝑖 n=4; i and 2 𝑖 2i are zeros; 𝑓 ( − 1 ) = 30 f(−1)=30 Answer 𝑖 i and 2 𝑖 2i be the zeros. So, − 𝑖 −i and − 2 𝑖 −2i be also zeros. 𝑓 ( 𝑥 ) is of 4th degree: f(x) is of 4th degree: 𝑓 ( 𝑥 ) = ( 𝑥 − 𝑖 ) ( 𝑥 + 𝑖 ) ( 𝑥 − 2 𝑖 ) ( 𝑥 + 2 𝑖 ) = ( 𝑥 2 + 1 ) ( 𝑥 2 + 4 ) . f(x)=(x−i)(x+i)(x−2i)(x+2i)=(x 2 +1)(x 2 +4). Expanding further: 𝑓 ( 𝑥 ) = ( 𝑥 2 + 1 ) ( 𝑥 2 + 4 ) = 𝑥 4 + 4 𝑥 2 + 𝑥 2 + 4 = 𝑥 4 + 5 𝑥 2 + 4. f(x)=(x 2 +1)(x 2 +4)=x 4 +4x 2 +x 2 +4=x 4 +5x 2 +4. Also, 𝑓 ( − 1 ) = ( − 1 ) 4 + 5 ( − 1 ) 2 + 4 = 1 + 5 + 4 = 10. f(−1)=(−1) 4 +5(−1) 2 +4=1+5+4=10.

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