If $\alpha$ is one of the roots of a quadratic equation $x^2-2px+p=0$, then the other root is equal to

Since alpha is a root of x^2 - 2px + p = 0, substituting it gives alpha^2 - 2p(alpha) + p = 0, which rearranges to p(1 - 2*alpha) = -alpha^2 and p = alpha^2 / (2*alpha - 1). By Vieta's formulas, the product of the roots of a quadratic equation equals the constant term divided by the leading coefficient, so alpha times the other root equals p. Substituting p = alpha^2 / (2*alpha - 1) gives alpha times the other root = alpha^2 / (2*alpha - 1), which simplifies to the other root = alpha / (2*alpha - 1).

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