Weierstrass Nullstellensatz

In mathematics, the Weierstrass Nullstellensatz is a version of the intermediate value theorem over a real closed field. It says: Given a polynomial f {\displaystyle f} in one variable with coefficients in a real closed field F and a < b {\displaystyle a<b} in F {\displaystyle F} , if f ( a ) < 0 < f ( b ) {\displaystyle f(a)<0<f(b)} , then there exists a c {\displaystyle c} in F {\displaystyle F} such that a < c < b {\displaystyle a<c<b} and f ( c ) = 0 {\displaystyle f(c)=0} .

Source: Wikipedia — Weierstrass Nullstellensatz (CC BY-SA 4.0)

Weierstrass Nullstellensatz

In mathematics, the Weierstrass Nullstellensatz is a version of the intermediate value theorem over a real closed field. It says: Given a polynomial f {\displaystyle f} in one variable with coefficients in a real closed field F and a < b {\displaystyle a<b} in F {\displaystyle F} , if f ( a ) < 0 < f ( b ) {\displaystyle f(a)<0<f(b)} , then there exists a c {\displaystyle c} in F {\displaystyle F} such that a < c < b {\displaystyle a<c<b} and f ( c ) = 0 {\displaystyle f(c)=0} .

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Source: Wikipedia "Weierstrass Nullstellensatz" · CC BY-SA 4.0

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