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
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Chapter2: Second-order Linear Odes
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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(x+ 4) + ( x+ 1 ) = 0

or, (x2 + 4)(x+ 1) = 0 ..(1) 

 

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