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(x-x1)(x-x2): Formula and Applications
Introduction
In algebra, the expression (x-x1)(x-x2) is a quadratic formula that represents a fundamental concept in mathematics. This formula is widely used in various mathematical concepts, such as equations, graphing, and functions. In this article, we will delve into the meaning and applications of (x-x1)(x2).
What is (x-x1)(x-x2)?
The formula (x-x1)(x-x2) is a quadratic expression that can be expanded into a polynomial of degree two. It represents the product of two binomials, where x is the variable, and x1 and x2 are constants.
(x-x1)(x-x2) = x^2 - (x1 + x2)x + x1x2
The formula can be interpreted as the difference of two squares, where x is the base, and x1 and x2 are the two factors.
Applications of (x-x1)(x-x2)
The formula (x-x1)(x-x2) has numerous applications in various fields, including:
Algebraic Equations
The formula is used to solve quadratic equations of the form ax^2 + bx + c = 0, where a, b, and c are constants. By factoring the quadratic expression, we can find the roots of the equation using the formula (x-x1)(x-x2).
Graphing and Functions
The formula is used to graph quadratic functions of the form f(x) = ax^2 + bx + c. By factoring the quadratic expression, we can find the x-intercepts of the graph using the formula (x-x1)(x-x2).
Physics and Engineering
The formula is used to model real-world phenomena, such as the trajectory of a projectile or the motion of an object under gravity. The formula helps to calculate the maximum height, range, and time of flight of a projectile.
Conclusion
In conclusion, the formula (x-x1)(x-x2) is a fundamental concept in algebra that has numerous applications in various fields. By understanding the formula and its applications, we can solve quadratic equations, graph functions, and model real-world phenomena.
