Jadhav Quadratic Formula

Jadhav Quadratic Formula, evaluates accurate values of numbers lying on x-axis of the co-ordinate plane corresponding to the respective y-axis points. Derived by Indian-Mathematical Scholar

Formula

If we are given the points of y-axis with the quadratic equation it followed then we can find the respective x-axis points by:

$x = {-b \pm \surd b^2 - 4a (c-y)}/2a$

Requirements

For this formula to function we should have the quadratic equation along with given y-axis point and can get the 2 corresponding points on the x-axis.

Nomenclature

  • b: Coefficient of $x$.
  • a: Coefficient of $x^2$.
  • c: Constant term of equation.
  • y: The given y-axis point.

Historical Note

This Formula is made by Jyotiraditya Abhay Jadhav, an Indian Mathematical-Scientist.

Derivation

Let the quadratic equation be : $ax^2+bx+c$

Now at some given value of x the function of graph will give the value for point lying on y-axis

So, we can equate

$ax^2+bx+c=y$

$x^2+bx/a+c/a = y/a$ (dividing all terms by a)

${x^{2}+2bx/2a+b^2/4a^2+c/a=y/a+b^2/4a^2}$ (adding ${b^2/4a^2}$ on both sides)

$[{x+b/2a}]^{2}+c/a=y/a+b^{2}/4a^{2}$

$[{x+b/2a}]^{2}=y/a+b^{2}/4a^{2}-c/a$

$x+b/2a=\pm\surd[y/a+b^{2}/4a^{2}-c/a]$

$x+b/2a=\pm\surd[4ay+b^{2}-4ac]/\surd\left\vert 4a^2 \right\vert$

$x=-b/2a\pm\surd[4ay+b^{2}-4ac]/\surd\left\vert 4a^2 \right\vert$

$x=[-b\pm\surd b^{2}-4a(c-y)]/2a$

Deriving the Jadhav Quadratic Formula.

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