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Use calculus to show that if f(x) = (x − a)²g(x), where both f(x) and g(x) are polynomials, then f(x) and f'(x) will have a factor in common.

Use calculus to show that if f(x) = (x − a)²g(x), where both f(x) and g(x) are polynomials, then f(x) and f'(x) will have a factor in common.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Complex Numbers
Section4.2: Complex Solutions Of Equations
Problem 7ECP: Find the cubic polynomial function f with real coefficients that has 1 and 2+i as zeros, and f2=2.
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Use calculus to show that if f(x) = (x − a) g(x), where both f(x) and g(x) are polynomials, then - f(x) and f'(x) will have a factor in common.
Transcribed Image Text:Use calculus to show that if f(x) = (x − a) g(x), where both f(x) and g(x) are polynomials, then - f(x) and f'(x) will have a factor in common.
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