In general, if \(\alpha\) and \(\beta\) are the zeroes of the quadratic polynomial \(p(x) = ax^2 + bx + c\), \(a \neq 0\), then you know that \(x - \alpha\) and \(x - \beta\) are the factors of \(p(x)\). Therefore, \(ax^2 + bx + c = k(x - \alpha)(x - \beta)\), where \(k\) is a constant. \(ax^2 + bx + c = k[x^2 - (\alpha + \beta)x + \alpha \beta] = kx^2 - k(\alpha + \beta)x + k \alpha \beta\). Comparing the coefficients of \(x^2, x\) and constant terms on both the sides, we get \(a = k, b = -k(\alpha + \beta)\) and \(c = k \alpha \beta\). This gives \(\alpha + \beta = \frac{-b}{a}\) and \(\alpha \beta = \frac{c}{a}\).