The discussion focuses on proving the relationship between the coefficients of two quadratic equations, specifically ax² + bx + c = 0 and a'x² + b'x + c' = 0, where the roots of the second equation are derived by adding a constant γ to the roots of the first equation. The key equation to prove is a′²(b² - 4ac) = a² + (b′² - 4a′c′). This proof involves manipulating the coefficients and applying the quadratic formula to establish the equality definitively.
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