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Quadratic equations are polynomial equations of degree two expressed in the form ax² + bx + c = 0. This section discusses the origins of solving quadratic equations, presents various examples, and explains how to represent word problems mathematically as quadratic equations, enhancing understanding through practical applications.
In this section, we explore quadratic equations, defined as equations in the form of ax² + bx + c = 0, where a, b, and c are real numbers, and a ≠ 0. Quadratic equations are prevalent in various real-world applications, such as determining dimensions in construction projects or calculating areas.
The section presents various examples illustrating how to mathematically represent problems as quadratic equations, emphasizing their significance and applications in daily life.
Quadratic Equation: An equation that can be expressed in the standard form ax² + bx + c = 0.
Real-world Application: Quadratic equations can model various real-life scenarios.
Identifying Equations: The importance of rearranging equations to ascertain if they are quadratic.
Roots or Solutions: The values that satisfy the quadratic equation.
When two x's we see, their power is two, in the quadratic equation, it’s what they can do.
Imagine a garden where the length is twice the breadth plus one. Finding the area gives us a puzzle that leads to a quadratic equation!
Ax Bx C: Always Expand Basics to create your equation!
Example of finding the area of a hall that leads to the equation 2x² + x - 300 = 0.
Example of determining two consecutive integers through a quadratic equation.
Identifying quadratic equations from various formats.
Term: Quadratic Equation
Definition: An equation of the form ax² + bx + c = 0 where a, b, and c are real numbers and a ≠ 0.
An equation of the form ax² + bx + c = 0 where a, b, and c are real numbers and a ≠ 0.
Term: Roots/Solutions
Definition: The values of x that satisfy the quadratic equation (i.e., make it true).
The values of x that satisfy the quadratic equation (i.e., make it true).
Term: Discriminant
Definition: The value b² - 4ac that determines the nature of the roots of a quadratic equation.
The value b² - 4ac that determines the nature of the roots of a quadratic equation.
Term: Standard Form
Definition: The arranged format of a quadratic equation as ax² + bx + c = 0.
The arranged format of a quadratic equation as ax² + bx + c = 0.
Term: Polynomial
Definition: An expression consisting of variables raised to whole-number powers and combined using addition, subtraction, and multiplication.
An expression consisting of variables raised to whole-number powers and combined using addition, subtraction, and multiplication.