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for ot 6 and m 2, 3, 4 Prove that (i) Pn (z) and Qn (z) have only real roots, (ii) for m 2 and n odd, P (z) and Qn (z) have a common root z* (identify it), (iii) for m 2 and n odd, if the respective roots are put in increasing order, each root of Pn (z) is less than the corresponding one of Qn (z) up to z* and vice versa thereafter. This problem arose as a… (More)