Newton's Formulae for Polynomials

Let $f(x) = x^n + (P_1)\frac{x^n}{x} + (P_2)\frac{x^n}{x^2} +...(P_n)$ be a polynomial function. Let $A_1, A_2, A_3..., A_n$ be the roots of the equation $f(x) = 0$

Letus define the term S(r) as $S(r) = (A_1)^r + (A_2)^r +...(A_n)^r$

Then,

For r < n : $S(r) + (P_1)S(r-1) + (P_2)S(r-2) +... + (P_r)S(0) = 0$

For r >= n : $S(r) + (P_1)S(r-1) + (P_2)S(r-2) +... + (P_n)S(r-n) = 0$

This might come in handy someday!

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$