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Solving Quadratic Equations with the Quadratic Formula

April 30, 2023 by sastry

Solving Quadratic Equations with the Quadratic Formula

Solving Quadratic Equations with the Quadratic Formula 1The solutions of some quadratic equations, ax2 + bx + c = 0 (a≠0) are not rational, and cannot be obtained by factoring. For such equations, the most common method of solution is the quadratic formula.
Solving Quadratic Equations with the Quadratic Formula 2

Note: The quadratic formula can be used to solve ANY quadratic equation, even those that can be factored. Be sure you know this very useful formula!!!
Examples:

Solving Quadratic Equations with the Quadratic Formula 3
Solving Quadratic Equations with the Quadratic Formula 4
Solving Quadratic Equations with the Quadratic Formula 5
Solving Quadratic Equations with the Quadratic Formula 6
Solving Quadratic Equations with the Quadratic Formula 7

Deriving the Quadratic Formula:

The quadratic formula is derived from the quadratic equation by a process called “completing the square”. Here is how it was developed:

Solving Quadratic Equations with the Quadratic Formula 8

Filed Under: Mathematics Tagged With: Solving Quadratic Equations with the Quadratic Formula

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