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## Homework Statement

[PLAIN]http://img443.imageshack.us/img443/3096/questiond.jpg [Broken]

## The Attempt at a Solution

If [itex]P(z)Q(z)=0[/itex] then

[itex]\displaystyle a_0b_0 + (a_0b_1 + a_1 b_0)z + ... + \left( \sum_{i=0}^k a_i b_{k-i} \right) z^k + ... + a_n b_m z^{n+m} =0[/itex]

Now what? Equate coefficients?

[itex]a_0 b_0 =0 \Rightarrow a_0 = 0 \; \text{or}\; b_0 = 0[/itex]

[itex]a_0 = 0 \Rightarrow a_1 b_0 =0 \Rightarrow a_1 = 0 \; \text{or}\; b_0 =0[/itex]

[itex]b_0 =0 \Rightarrow a_0 b_1 = 0 \Rightarrow b_1 = 0 \; \text{or}\; a_0 = 0[/itex]

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