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Questions and Answers
What is the general form of an algebraic equation?
What is the general form of an algebraic equation?
What is the degree of the quadratic equation x^2 + 4x + 4 = 0?
What is the degree of the quadratic equation x^2 + 4x + 4 = 0?
What method can be used to solve the equation x^2 + 5x + 6 = 0?
What method can be used to solve the equation x^2 + 5x + 6 = 0?
What property allows us to add or subtract equations as long as they have the same variables and coefficients?
What property allows us to add or subtract equations as long as they have the same variables and coefficients?
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What is the formula used to solve quadratic equations?
What is the formula used to solve quadratic equations?
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What type of equation is x^3 - 2x^2 - 5x + 1 = 0?
What type of equation is x^3 - 2x^2 - 5x + 1 = 0?
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Study Notes
Algebraic Equations
Definition
- An algebraic equation is an equation involving variables and constants, and only uses addition, subtraction, multiplication, and division.
- It is written in the form: ax^n + bx^(n-1) + ... + cx + d = 0, where a, b, ..., c, d are constants and x is the variable.
Types of Algebraic Equations
- Linear Equations: Degree of the equation is 1 (e.g. 2x + 3 = 5)
- Quadratic Equations: Degree of the equation is 2 (e.g. x^2 + 4x + 4 = 0)
- Cubic Equations: Degree of the equation is 3 (e.g. x^3 - 2x^2 - 5x + 1 = 0)
- Polynomial Equations: Degree of the equation is greater than 3 (e.g. x^4 - 3x^3 + 2x^2 - x + 1 = 0)
Solving Algebraic Equations
- Factoring: Expressing the equation as a product of simpler expressions (e.g. x^2 + 5x + 6 = (x + 3)(x + 2) = 0)
- Quadratic Formula: x = (-b ± √(b^2 - 4ac)) / 2a, used to solve quadratic equations
- Graphical Method: Solving equations by finding the points of intersection between the graph of the equation and the x-axis
Properties of Algebraic Equations
- Addition and Subtraction: Equations can be added or subtracted, as long as they have the same variables and coefficients.
- Multiplication and Division: Equations can be multiplied or divided, as long as they have the same variables and coefficients.
- Distributive Property: a(b + c) = ab + ac, used to expand equations.
Algebraic Equations
- Algebraic equations involve variables and constants, and only use addition, subtraction, multiplication, and division.
Definition and Form
- The general form of an algebraic equation is ax^n + bx^(n-1) +...+ cx + d = 0.
- In this form, a, b,..., c, d are constants, and x is the variable.
Types of Algebraic Equations
- Linear Equations: Have a degree of 1, such as 2x + 3 = 5.
- Quadratic Equations: Have a degree of 2, such as x^2 + 4x + 4 = 0.
- Cubic Equations: Have a degree of 3, such as x^3 - 2x^2 - 5x + 1 = 0.
- Polynomial Equations: Have a degree greater than 3, such as x^4 - 3x^3 + 2x^2 - x + 1 = 0.
Solving Algebraic Equations
- Factoring: Involves expressing the equation as a product of simpler expressions, such as x^2 + 5x + 6 = (x + 3)(x + 2) = 0.
- Quadratic Formula: x = (-b ± √(b^2 - 4ac)) / 2a, used to solve quadratic equations.
- Graphical Method: Solves equations by finding the points of intersection between the graph of the equation and the x-axis.
Properties of Algebraic Equations
- Addition and Subtraction: Equations can be added or subtracted if they have the same variables and coefficients.
- Multiplication and Division: Equations can be multiplied or divided if they have the same variables and coefficients.
- Distributive Property: a(b + c) = ab + ac, used to expand equations.
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Description
Learn about algebraic equations, including linear and quadratic equations, and their definitions and types. Understand the forms of equations and how to work with them.
