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Your solution is a lot neater than that.chwala said:
Solving a quadratic equation as a sum and product of its roots
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The discussion revolves around solving a quadratic equation using the sum and product of its roots, specifically addressing the confusion regarding the signs in the coefficients of the resulting equation. Participants clarify that the sum of the roots, expressed as ##\frac{1}{\alpha^3} + \frac{1}{\beta^3}##, should yield a positive coefficient for the x-term in the new equation, contrary to the initial interpretation of a negative sign. The correct formulation leads to the equation ##c^3x^2 + b(b^2 - 3ac)x + a^3 = 0##, aligning with the textbook solution. The importance of checking calculations and understanding the relationship between roots and coefficients is emphasized, highlighting that different problems may yield different signs. Ultimately, the participants reach a consensus on the correct interpretation and application of the quadratic formula.
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