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Let y=f(x) be a cubic polynomial with leading coefficient, a=1; containing the ordered pair (2,0) and a zero at x=2i. Find the function, f(x), that has these characteristics.

Let y=f(x) be a cubic polynomial with leading coefficient, a=1; containing the ordered pair (2,0) and a zero at x=2i. Find the function, f(x), that has these characteristics.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let y=f(x) be a cubic polynomial with leading coefficient, a=1; containing the ordered pair (2,0) and a zero at x=2i. Find the function, f(x), that has these characteristics.
**MAT 171: Sections 2.3–2.5 Lab** 2. Let \( y = f(x) \) be a cubic polynomial with leading coefficient, \( a = -1 \); containing the ordered pair \( (2, 0) \), and a zero at \( x = 2i \). Find a function, \( f(x) \), that has these characteristics. 3. Given: \( f(x) = (3x^5 - 5x^2 + 3)(x^2 - 6x - 6) \) a. What is the parent function? b. How many zeros will this function have in total (both real and complex)? c. What is the domain of this function, in interval notation? d. What is the range of this function, in interval notation? 4. Find all zeros of the function, \( g(x) = x^3 - 7x^2 - x + 87 \), given that \( 5 + 2i \) is a zero. **Note**: The document is focused on polynomial functions, requiring the analysis of characteristics like zeros, domain, and range.
Transcribed Image Text:**MAT 171: Sections 2.3–2.5 Lab** 2. Let \( y = f(x) \) be a cubic polynomial with leading coefficient, \( a = -1 \); containing the ordered pair \( (2, 0) \), and a zero at \( x = 2i \). Find a function, \( f(x) \), that has these characteristics. 3. Given: \( f(x) = (3x^5 - 5x^2 + 3)(x^2 - 6x - 6) \) a. What is the parent function? b. How many zeros will this function have in total (both real and complex)? c. What is the domain of this function, in interval notation? d. What is the range of this function, in interval notation? 4. Find all zeros of the function, \( g(x) = x^3 - 7x^2 - x + 87 \), given that \( 5 + 2i \) is a zero. **Note**: The document is focused on polynomial functions, requiring the analysis of characteristics like zeros, domain, and range.
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