The ABC Formula: Solving Quadratic Equations Made Easy
What is the ABC Formula?
The ABC formula is a nifty mathematical tool that helps you solve quadratic equations. In elementary algebra, a quadratic equation is an equation that can be written in the form ax2 + bx + c = 0, where a, b, and c are constants. The ABC formula provides a closed-form expression for the solutions to such equations.
Solving Quadratic Equations with the ABC Formula
To solve a quadratic equation using the ABC formula, you need to know the values of a, b, and c. Once you have these values, you can plug them into the formula and solve for x:
x = (-b ± √(b2 - 4ac)) / 2a
The ± symbol means that there are two possible solutions for x. You can find both solutions by plugging in the values of a, b, and c and evaluating the expression.
For example, let's say we want to solve the quadratic equation x2 - 5x + 6 = 0. Using the ABC formula, we get:
x = (-(-5) ± √((-5)2 - 4(1)(6))) / 2(1)
x = (5 ± √(25 - 24)) / 2
x = (5 ± 1) / 2
x = 2 or x = 3
So, the solutions to the quadratic equation x2 - 5x + 6 = 0 are x = 2 and x = 3.
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