Find all the roots of f(x). Use the zeros of f(x) to write the factored form. f(x) = x4 + 5x2 + 4
Find all the roots of f(x). Use the zeros of f(x) to write the factored form. f(x) = x4 + 5x2 + 4
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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Question
Find all the roots of f(x). Use the zeros of f(x) to write the factored form.
f(x) = x4 + 5x2 + 4
Expert Solution
Step 1
The roots of f(x) = x4 + 5x2 + 4 are the solution of f(x) = 0.
f(x) = 0 gives
x4 + 5x2 + 4 = 0
or, (x2 )2 + 4x2 + x2 + 4 = 0
or, x2(x2 + 4) + ( x2 + 1 ) = 0
or, (x2 + 4)(x2 + 1) = 0 ..(1)
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