# proof of Vieta’s formula

Proof: We can write $P(x)$ as

 $P(x)=a_{n}(x-r_{1})(x-r_{2})\ldots(x-r_{n})=a_{n}(x^{n}-S_{1}x^{n-1}+S_{2}x^{n% -2}-\ldots+(-1)^{n}S_{n}).$

Since we also have that

 $P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\ldots a_{1}x+a_{0},$

setting the coefficients equal yields

 $a_{n}(-1)^{i}S_{i}=a_{n-i}$

which is what the theorem stated.

Title proof of Vieta’s formula ProofOfVietasFormula 2013-03-22 15:26:59 2013-03-22 15:26:59 neapol1s (9480) neapol1s (9480) 4 neapol1s (9480) Proof msc 12Y05