Geometry of Polynomial Roots

For a quadratic polynomial $p (x) = x^{2} + b x + c$ with roots $z_{1}$ and $z_{2}$ , the coefficients are given by $b = - (z_{1} + z_{2})$ and $c = z_{1} z_{2}$ .

Proof. Expand $p (x) = (x - z_{1}) (x - z_{2}) .$

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