(2) Complex roots: (a) Check that z is a product of linear factors over C. (b) Check that all four of z = ±(i) satisfy z4 = -1. Confirm that z4+1 is a product of linear factors over C. (c) We know that =b±vb-4ac are the roots of az² + bz + c if a,b, c € R ±1 and z = ti all satisfy zª = 1. Confirm that z4– 1 %3D 2a -b±i/[6²–4ac[| and b2 – 4ac > 0. Check that b? – 4ac < 0. Confirm that this quadratic factors as a product of linear factors over C. are complex roots, if 2a -

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.3: Quadratic Equations
Problem 82E
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the image below is the question. Thank you. This is Math 3001 Real Analysis II

(2) Complex roots:
(a) Check that z
is a product of linear factors over C.
(b) Check that all four of z = +() satisfy z4 = -1. Confirm that 24+1
is a product of linear factors over C.
(c) We know that
±1 and z = ±i all satisfy z4 = 1. Confirm that z4 – 1
-b+v–4ac
are the roots of az? + bz + c if a, b, c e R
2a
-btiv62-4ac|
and b? – 4ac > 0. Check that
b? – 4ac < 0. Confirm that this quadratic factors as a product of
linear factors over C.
are complex roots, if
2a
Transcribed Image Text:(2) Complex roots: (a) Check that z is a product of linear factors over C. (b) Check that all four of z = +() satisfy z4 = -1. Confirm that 24+1 is a product of linear factors over C. (c) We know that ±1 and z = ±i all satisfy z4 = 1. Confirm that z4 – 1 -b+v–4ac are the roots of az? + bz + c if a, b, c e R 2a -btiv62-4ac| and b? – 4ac > 0. Check that b? – 4ac < 0. Confirm that this quadratic factors as a product of linear factors over C. are complex roots, if 2a
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