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2. Let char F = 0 and f(x) E F[x] be a monic polynomial having positive degree. If d(x) = gcd(f(x), f'(x)), then prove that g(x) = 9 has the same roots as f(x) and g(x) is separable. %3D (x)p

2. Let char F = 0 and f(x) E F[x] be a monic polynomial having positive degree. If d(x) = gcd(f(x), f'(x)), then prove that g(x) = 9 has the same roots as f(x) and g(x) is separable. %3D (x)p

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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2. Let char F = 0 and f(x) E F[x] be a monic polynomial having positive degree. If that g(x) = f (x) d(x) = gcd(f(x), f'(x)), g(x) is separable. has the same roots as f(x) and (x)p then prove ||
Transcribed Image Text:2. Let char F = 0 and f(x) E F[x] be a monic polynomial having positive degree. If that g(x) = f (x) d(x) = gcd(f(x), f'(x)), g(x) is separable. has the same roots as f(x) and (x)p then prove ||
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