Find the roots of the quadratic equation by differentiation

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SUMMARY

The discussion focuses on solving quadratic equations using differentiation, specifically highlighting the method of finding the symmetry axis of a parabola represented by the equation ax² + bx + c. The key takeaway is that by determining the x-coordinate of the vertex (minimum or maximum) and calculating the distance to the roots, one can effectively find the zeros of the quadratic equation. This method, while more complex than completing the square, provides a valid approach to understanding parabolic functions.

PREREQUISITES
  • Understanding of quadratic equations and their standard form (ax² + bx + c)
  • Basic knowledge of calculus, specifically differentiation
  • Familiarity with the properties of parabolas
  • Ability to interpret graphical representations of functions
NEXT STEPS
  • Study the concept of the vertex of a parabola in detail
  • Learn about the method of completing the square for quadratic equations
  • Explore advanced differentiation techniques and their applications
  • Research the graphical interpretation of quadratic functions and their roots
USEFUL FOR

Students, mathematicians, and educators interested in advanced methods for solving quadratic equations and understanding parabolic functions through calculus.

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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