Quadratic Formula Derivation

Derivation of Quadratic Formula

The roots of a quadratic equation ax2 + bx + c = 0 is given by the quadratic formula

The derivation of this formula can be outlined as follows:

1. Divide both sides of the equation ax2 + bx + c = 0 by a.
2. Transpose the quantity c/a to the right side of the equation.
3. Complete the square by adding b2 / 4a2 to both sides of the equation.
4. Factor the left side and combine the right side.
5. Extract the square-root of both sides of the equation.
6. Solve for x by transporting the quantity b / 2a to the right side of the equation.
7. Combine the right side of the equation to get the quadratic formula.

Quadratic Formula helps to evaluate the solution of quadratic equations replacing the factorization method.

The general form of a quadratic equation is ax2 + bx + c = 0, where a, b and c are real numbers, also called “numeric coefficients”.

Here x is an unknown variable for which we need to find the solution.

Quadratic Formula is also known as Shreedhara Acharya’s formula.

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