For a quadratic polynomial \(p(x) = x^2 + bx + c\) with roots \(z_1\) and \(z_2\), the coefficients are given by \(b = -(z_1 + z_2)\) and \(c = z_1z_2\).

Proof. Expand \(p(x) = (x-z_1)(x-z_2).\)