I Find the roots of the quadratic equation by differentiation

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The discussion explains that the roots of a quadratic equation can be found using differentiation by identifying the x-coordinate of the vertex of the parabola, which represents the minimum or maximum point. This method involves calculating the distance to the zeros of the equation. While the differentiation approach is valid, it is noted that it is more complex compared to simpler methods like completing the square. Additionally, there is a reference to further reading on parabolas for those interested. The overall consensus is that while this method works, it is not the most straightforward approach.
Anurag yadav
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The Solution of the Quadratic Equation By Differentiation Method
 

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Anurag yadav said:
The Solution of the Quadratic Equation By Differentiation Method
Yes, that can be done. A quadratic equation ##(x\, , \,ax^2+bx+c)## is a parabola. You basically computed where the symmetry axis of a standard parabola lies by determining the x-coordinate of the minimum (##a>0##) or maximum (##a<0##), and then the distance to its two zeros (so they exist). Maybe you are interested to read more about parabolas. https://en.wikipedia.org/wiki/Parabola
 
What is your goal? The method is not really new, only a bit more complicated than e.g. completing the square.

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