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 ${\displaystyle f}$ in one variable with coefficients in a real closed field F and ${\displaystyle a<b}$ in ${\displaystyle F}$, if ${\displaystyle f(a)<0<f(b)}$, then there exists a ${\displaystyle c}$ in ${\displaystyle F}$ such that ${\displaystyle a<c<b}$ and ${\displaystyle f(c)=0}$.