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The four points A(alpha, 0), B(beta, 0),...

The four points `A(alpha, 0), B(beta, 0), C(gamma, 0)` and `D(delta, 0)` are such that `alpha, beta` are the roots of equation `ax^(2)+2h x + b=0`, and `gamma, delta` are the roots of equation `a' x^(2)+2h' x + b'=0`. Show that the sum of the ratios in which C and D divide AB is zero, if `ab' + a' b = 2hh'`.

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