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A cubic equation f(x) = 0 has one real root a and two a, ß+iy and B-iy respectively on the Argand diag

A cubic equation f(x) = 0 has one real root a and two a, ß+iy and B-iy respectively on the Argand diag

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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A cubic equation f(x) = 0 has one real root a and two complex roots ß ±iy. Points A, B, C represent roots a, ß+iy and ß-iy respectively on the Argand diagram. Show that the roots of the equation f'(x) = 0 (the left hand side is the derivative off) are complex if A falls inside one of the two equilateral triangles described on base BC.
Transcribed Image Text:A cubic equation f(x) = 0 has one real root a and two complex roots ß ±iy. Points A, B, C represent roots a, ß+iy and ß-iy respectively on the Argand diagram. Show that the roots of the equation f'(x) = 0 (the left hand side is the derivative off) are complex if A falls inside one of the two equilateral triangles described on base BC.
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