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Jadhav Quadratic Formula

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Jadhav Quadratic Formula
Modified Conventional Quadratic Formula
Definition
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 Jyotiraditya Jadhav
Details
Indian Invention

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 Jyotiraditya Jadhav.

Formula[edit]

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:

here the plus-minus "±" indicated the quadratic equation has two solutions. written separately, they become.

and

Been a quadratic equation each point at a height of y-axis will have two x-axis points, following the rules or discriminant.

Rule[edit]

if then the equation does not have solution in real numbers.

if then the equation have solutions in real numbers.

if then the y-axis point is at the end of the parabola and is at center so has only one solution.

The "Conventional" Quadratic Formula[edit]

Roots of a quadratic function
A quadratic function with roots x = 1 and x = 4.

In elementary algebra, the quadratic formula is a formula that provides the solution(s) to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring (direct factoring, grouping, AC method), completing the square, graphing and others.[1]

Given a general quadratic equation of the form

with x representing an unknown, a, b and c representing constants with a ≠ 0, the quadratic formula is:

where the plus-minus symbol "±" indicates that the quadratic equation has two solutions.[2] Written separately, they become:

Each of these two solutions is also called a root (or zero) of the quadratic equation. Geometrically, these roots represent the x-values at which any parabola, explicitly given as y = ax2 + bx + c, crosses the x-axis.[3]

As well as being a formula that yields the zeros of any parabola, the quadratic formula can also be used to identify the axis of symmetry of the parabola,[4] and the number of real zeros the quadratic equation contains.[5]

Proving the "Constant method"[edit]

Jadhav Quadratic Formula also proves the "Constant method" of Conventional Quadratic Formula. If the equation was equated to some value of y non-zero then the new constant becomes and we can even apply conventional quadratic formula to it of constant c been which becomes Jadhav Quadratic Formula.

Requirements[edit]

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[edit]

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

Historical Note[edit]

This Formula is made by Jyotiraditya Abhay Jadhav, an Indian Mathematical-Scientist. The story revolves of him been trying to derive Quadratic Formula with different methods of divisional process and thought of other values of y-axis instead of 0 (roots of quadratic equation) and denoted it with "y" and later derived to this equation of equating value of "x" to respective coefficient of the equation with "y".

Derivation[edit]

Let the quadratic equation be :

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

(dividing all terms by a)

(adding on both sides)

Deriving the Jadhav Quadratic Formula.

  1. "Quadratic Factorisation: The Complete Guide". Math Vault. 2016-03-13. Retrieved 2019-11-10.
  2. Sterling, Mary Jane (2010), Algebra I For Dummies, Wiley Publishing, p. 219, ISBN 978-0-470-55964-2
  3. "Understanding the quadratic formula". Khan Academy. Retrieved 2019-11-10.
  4. "Axis of Symmetry of a Parabola. How to find axis from equation or from a graph. To find the axis of symmetry ..." www.mathwarehouse.com. Retrieved 2019-11-10.
  5. "Discriminant review". Khan Academy. Retrieved 2019-11-10.