The term equation means equating one quantity with the other. Algebraic equations are mathematical statements that represent terms that are equal to each other. These algebraic terms can have variables, constants, and arithmetic operators like addition, multiplication, etc. For instance, Polynomial equations are among the most common forms of algebraic equations that involve equating polynomials. There are some other types of algebraic equations based on variable, operator type, and functions.
Learning algebra equations help in converting various word problems into their mathematical forms. Once you learn to recognize the equation’s type, you can easily apply rules to solve them. These algebraic equations have varying inputs and outputs with different interpretations. There are five different types of algebraic equations that demonstrate the use of algebraic operations.
Monomial/Polynomial Equations
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Polynomials equations are algebraic equations that comprise polynomial expressions. These expressions involve terms with whole numbers as exponents. Polynomials are of different types based on the number of terms present in these expressions: Monomial is a polynomial with one term, binomial is a polynomial with two terms, trinomial has three terms. Polynomials are also categorized based on their degree, which means the highest exponent in the expression. Polynomials with degree one are called linear polynomials and polynomials with degrees two and three are called quadratic, and cubic polynomials. For example, an equation with polynomial x – 3 is called a linear binomial.
Exponential Equations
Exponential equations are equations that have variables in their exponents. They are different from polynomials since they have variable terms in the exponents. For example, equation y = 5^(x – 3) + 8 is an exponential equation with variable exponent. The independent variable in an exponent function with a positive coefficient signifies exponential growth, and a negative coefficient signifies exponential decay.
The exponential growth equations are applied in calculating various growth aspects like the spread of populations or diseases. It is also used in various financial concepts to calculate compound interest, whereas the exponential decay equations are suitable to represent phenomena like radioactive decay.
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Logarithmic Equations
Logarithmic equations are algebraic equations with logarithmic functions that are inverse of exponential functions. These equations are applied in several kinds of intensity scales, like the Richter scale used for earthquakes and the decibel scale used for sound intensity. The decibel scale utilizes a log base of 10, implying a rise of one decibel corresponds to a ten times increase in sound intensity.
Rational Equations
Rational equations are algebraic equations that are in a form of m(x) / n(x), where both m(x) and n(x) are polynomials. An example of a rational equation is (x – 3) / (x^2 – 9x + 8). Rational equations are used to solve many problems based on valuations, times, and work. Rational expressions and equations are helpful to determine how to correlate workers or machines to finish a task for a schedule.
Trigonometric Equations
Trigonometric equations are algebraic equations that comprise trigonometric functions like sin, cos, tan, sec, cosec, and cot. Trigonometric functions define a ratio of two sides of a right triangle, taking the angle measure as the input or independent variable and the ratio as the output or dependent variable.
Understanding and solving algebra equations requires focus and knowledge of fundamental concepts. As this topic is a little difficult for kids to learn, it needs more attention and practice. By practising a variety of problems based on these algebraic equations, students can readily attain the focus and the key skills required for solving each type of algebraic equation. Cuemath provides learning resources for students to improve their algebra knowledge with ease. To find some of these interactive algebra resources, visit website.
