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Suppose $w$ is a complex number, and set $c=\max(1,|w|)$. If $F$ and $G$ are non-zero polynomials in one indeterminate with coefficients in $\mathbb{C}$, and $\deg(F)=d$ and $\deg(G)=d'$, with $|F|,|G|\geq 1$. If $R$ is their resultant, then why is $$ |R|\leq c^{d+d'}[|F(w)|+|G(w)|]|F|^{d'}|G|^d(d+d')^{d+d'}? $$

Here, I'm using $|F|$ to be the maximum of the absolute values of the coefficients of $F$. Thanks for any suggestions on approaching this.

The Source of this problem is Serge Lang's Algebra, exercise 16 of Chapter IV.

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Could you indicate why you believe this is true ? Or, maybe, give a reference where such an inequality is stated. – Sasha Nov 22 '11 at 20:35
In your inequality, should $|R|$ be $|R(w)|$? Otherwise, why is the right hand side related to #\$w$? – Paul Nov 22 '11 at 23:29
@Sasha Sure, I will do that. – Clara Nov 24 '11 at 13:18
Must be a different edition. Chapter IV of my copy of Lang's Algebra is Homology, and the only exercise in it is the notorious one, "Take any book on homological algebra, and prove all the theorems without looking at the proofs given in that book." Found it! In my edition, it's Chapter V, exercise 13. – Gerry Myerson Nov 25 '11 at 0:05

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