Exercise 1.

Find all real roots and their multiplicity of the polynomial

displaymath23

Answer.

The polynomial f(x) has root x=1 with multiplicity 2.

2x+5=0 if x=-5/2; Consequently f(x) has the root x=-5/2, with multiplicity 3.

The polynomial tex2html_wrap_inline37 is irreducible; here is its graph again:

Finally, the term tex2html_wrap_inline39 , when tex2html_wrap_inline41 . Thus f(x) has the root tex2html_wrap_inline41 , with multiplicity 4.

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Helmut Knaust
Tue Jun 10 17:34:08 MDT 1997

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