Difference between revisions of "Jadhav Quadratic Formula"

Revision as of 09:22, 2 February 2025

The Jadhav Quadratic Formula finds all values of $x$ for a given value of $y$ in any quadratic equation $ax^2+bx+c$ . It is named after mathematician Jyotiraditya Jadhav.

Statement

For any given value of $y$ in quadratic equation $y=ax^2+bx+c$ , we can find its respective values for $x$

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

Derivation

We have the quadratic equation $y = ax^2+bx+c$ , which can be rewritten as $ax^2+bx+(c-y) = 0$ . From the quadratic formula, we have $x = \frac{-b \pm \sqrt{b^2-4a(c-y)}}{2a}$ , as desired.

@@ Line 1: / Line 1: @@
-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
+The '''Jadhav Quadratic Formula''' finds all values of <math>x</math> for a given value of <math>y</math> in any [[quadratic equation]] <math>ax^2+bx+c</math>. It is named after mathematician [[Jyotiraditya Jadhav]].
-== '''Formula''' ==
+== Statement ==
-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:
-<math>x = {-b \pm \surd b^2 - 4a (c-y)}/2a</math>
+For any given value of <math>y</math> in quadratic equation <math>y=ax^2+bx+c</math>, we can find its respective values for <math>x</math>
-== Requirements ==
+<cmath>x = \frac{-b \pm \sqrt{b^2-4a(c-y)}}{2a}</cmath>
-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 ==
+=== Derivation ===
-* '''b: Coefficient of <math>x</math>.'''
+We have the quadratic equation <math>y = ax^2+bx+c</math>, which can be rewritten as <math>ax^2+bx+(c-y) = 0</math>. From the [[quadratic formula]], we have <math>x = \frac{-b \pm \sqrt{b^2-4a(c-y)}}{2a}</math>, as desired.
-* '''a: Coefficient of <math>x^2</math>.'''
-* '''c: Constant term of equation.'''
-* '''y: The given y-axis point.'''
-== Historical Note ==
+== See Also ==
-This Formula is made by '''[[Jyotiraditya Jadhav|Jyotiraditya Abhay Jadhav]],''' an Indian Mathematical-Scientist.
-== Derivation ==
+* [[Quadratic Equation]]
-Let the quadratic equation be : <math>ax^2+bx+c </math>
+* [[Quadratic Formula]]
-Now at some given value of x the function of graph will give the value for point lying on y-axis
+{{stub}}
-So, we can equate
-<math>ax^2+bx+c=y </math>
-<math>x^2+bx/a+c/a = y/a   </math> (dividing all terms by a)
-<math>{x^{2}+2bx/2a+b^2/4a^2+c/a=y/a+b^2/4a^2} </math> (adding <math>{b^2/4a^2} </math> on both sides)
-<math>[{x+b/2a}]^{2}+c/a=y/a+b^{2}/4a^{2}
- </math>
-<math>[{x+b/2a}]^{2}=y/a+b^{2}/4a^{2}-c/a
- </math>
-<math>x+b/2a=\pm\surd[y/a+b^{2}/4a^{2}-c/a]
- </math>
-<math>x+b/2a=\pm\surd[4ay+b^{2}-4ac]/\surd\left\vert 4a^2 \right\vert
- </math>
-<math>x=-b/2a\pm\surd[4ay+b^{2}-4ac]/\surd\left\vert 4a^2 \right\vert
- </math>
-<math>x=[-b\pm\surd b^{2}-4a(c-y)]/2a
- </math>
-Deriving the Jadhav Quadratic Formula.
-[[Category:Jyotiraditya Jadhav]]
-[[Category:Mathematical concepts]]
-__INDEX__

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Difference between revisions of "Jadhav Quadratic Formula"

Revision as of 09:22, 2 February 2025

Statement

Derivation

See Also