In Mathematics, an equation is defined as an algebraic expression in which one side of the expression should be equal to the expression on the other side. Equations follow the logic of the balance scale. The equation is considered as an inequality if the expression on one side is not equal to the other side. Like algebraic expressions, equations also contain coefficients, constants, variables, terms, mathematical operators, exponents, etc. In addition to all these parameters, the equation should have an equal sign “=” between the expressions.
There are different types of equations, such as quadratic equations, polynomial equations, trigonometric equations, linear differential equations, cubic equations, partial differential equations, etc. Now, let us discuss the different types of equations in Maths with examples.
A polynomial equation is a kind of algebraic equation in which the expression comprises multiple constants and variables. The polynomial equation can be any type like monomial equation (linear equation), binomial equation (quadratic equation), trinomial equation (cubic equation) or any higher-order degree equation. The highest power of the variable in the equation is called the degree of the equation.
The polynomial equation of degree 2 is called the binomial or quadratic equation. Generally, the quadratic equation has two roots. The nature of the roots can be determined using the discriminant value, which may be either real or imaginary. We know that the quadratic polynomial is in the form of ax2+bx+ c, where a is not equal to 0. When the quadratic polynomial is equated to 0, it becomes a quadratic equation. Thus, the general form of the quadratic equation is ax2+bx+c =0.
An algebraic equation of degree 3 is called the cubic equation. The cubic equation has three roots. Unlike quadratic equations, a cubic equation should have at least one real root. The other roots may be real or imaginary. The general form of the cubic equation is ax3+bx2+cx+d =0, where a ≠ 0.
Generally, cubic equations and the higher-order degree equations can be solved by reducing them into quadratic equations.
A differential equation is an equation that involves the derivatives of the dependent variable with respect to the independent variable. Based on the order, type, linearity and homogeneity, the differential equations are classified as first and second-order differential equations, partial and ordinary differential equations, linear and nonlinear differential equations, homogeneous and nonhomogeneous differential equations.
An equation that involves the variables with trigonometric functions is called trigonometric equations. An equation can have any trigonometric functions like sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec) and cotangent (cot). If a trigonometric equation has functions like cosecant, secant and cotangent functions, these are generally converted into the primary functions like sine, cosine and tangent, respectively.
An example of the trigonometric function is sin 4x=0.
Some of the trigonometric equations do not satisfy all the values of the x. For such kind of equations, we have to find the values of x.
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