A Quadratic equation is a second degree polynominal equation in one variable that is generally expressed as ax2+bx+c=0, where a,b, and c are constants and "x" is the variable. The quadratic formula provides the answers to a quadratic equation :

X=[-b (b2-4ac) ]/2a]

Three sorts of solutions can be found for quadratic equations :

a. If the discriminants (b2-4ac) is positive, there are two unique real solution.

b. If the discriminants is 0, there is only one real solution.

c. Two intricate answers if the discriminant is unfavourable.

Numerous fields, including mathematics, physics, engineering, and a number of others, use quadratic equations extensively.

Additional special functions and equations :

1. Linear Equations (a) :-

A first-degree polynominal equation with a single variable is a linear equation. In this equation,  "a" and "b" are constants, and the form is ax+b=0. A linear equation has the simple solution x=-b/a.

2. Exponential Equations :-

Exponential equations are equations in which the variable is contained inside the exponent. It can take on a number of shapes, such as a function of thetype f(x)=ax where "a" is a constant base or a function of the form ax=b where "a" and "b" are constants. Exponent value calculations and base identification are frequent steps in solving exponential equations.

3. Logarithmic Equations :-

A logarithmic equation is a mathematical formula in which the variable is a logarithmic function. It can have several shapes, such as log-a(x)=b, where "a" stands for the logarithm's base, "x" for the variable, and "b" for a fixed value. In order to solve logarithmic equations, one must firstchange them into exponential form.

4. Trigonometric Functions :-

Trigonometric functions,such as sine, cosine, tangent, etc, are used in trigonometric equations. When "a", "b", and "c" are constants, they can take the form sin(x)=a, cos(x)=b, or tan(x)=c. Trigonometric identities and the periodicity of trigonometric functions are frequently used in the solution of trigonometric equations.

5. Absolute Value Equations :-

An equation that contains an absolute value expression, such as |x|=a, where "a" is a constant, is referred to as an absolute value equation. Depending on how "a" is written, absolute value equations can have a variety of answers and contain situations where x can be either positive or negative.

There are but a handful of illustrations of unique equations and functions. Each type has unique characteristics, approaches to solving problems, and applications across severel academic disciplines.