here is the solution I got but I do not know where 8x(x+1) came from in step one: Find all roots of f(x). f(x)= -x6+x5-2x4+4x3+8x2 Expert Solution arrow_forward Step 1 We have f(x) = -x6 + x5 -2x4 + 4x3 + 8x2 = - x5 (x+1) + 2x4 (x+1) - 4x3 (x+1) + 8x2 (x+1) arrow_forward Step 2 So, f(x) = x2 (x+1) ( - x3 +2x2 - 4x + 8) = x2 (x+1) { - x2 (x -2) - 4 (x -2) } = - x2 (x +1) (x -2) (x2 +4) = - x2 (x +1) (x -2) { (x+2i)(x-2i)} So, the roots of f(x) are x = -1, 0, 0, 2, -2i, 2i. So, f(x) has 4 real roots and 2 complex roots.
here is the solution I got but I do not know where 8x(x+1) came from in step one: Find all roots of f(x). f(x)= -x6+x5-2x4+4x3+8x2 Expert Solution arrow_forward Step 1 We have f(x) = -x6 + x5 -2x4 + 4x3 + 8x2 = - x5 (x+1) + 2x4 (x+1) - 4x3 (x+1) + 8x2 (x+1) arrow_forward Step 2 So, f(x) = x2 (x+1) ( - x3 +2x2 - 4x + 8) = x2 (x+1) { - x2 (x -2) - 4 (x -2) } = - x2 (x +1) (x -2) (x2 +4) = - x2 (x +1) (x -2) { (x+2i)(x-2i)} So, the roots of f(x) are x = -1, 0, 0, 2, -2i, 2i. So, f(x) has 4 real roots and 2 complex roots.
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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here is the solution I got but I do not know where 8x(x+1) came from in step one:
Find all roots of f(x).
f(x)= -x6+x5-2x4+4x3+8x2
Expert Solution
arrow_forward
Step 1
We have f(x) = -x6 + x5 -2x4 + 4x3 + 8x2
= - x5 (x+1) + 2x4 (x+1) - 4x3 (x+1) + 8x2 (x+1)
arrow_forward
Step 2
So, f(x) = x2 (x+1) ( - x3 +2x2 - 4x + 8)
= x2 (x+1) { - x2 (x -2) - 4 (x -2) }
= - x2 (x +1) (x -2) (x2 +4)
= - x2 (x +1) (x -2) { (x+2i)(x-2i)}
So, the roots of f(x) are
x = -1, 0, 0, 2, -2i, 2i.
So, f(x) has 4 real roots and 2 complex roots.
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