# Types of Equations

## 1. Polynomial Equations

Polynomial equations are in the form P(x) = 0, where P(x) is a polynomial.

## Types of Polynomial Equations

### 1.1 Linear Equations

Linear equations are equations of the type ax + b = 0, with a ≠ 0, or any other equation in which the terms can be operated and simplified into an equation of the same form.

(x + 1)^{2} = x^{2} - 2

x^{2} + 2x + 1 = x^{2} - 2

2x + 1 = -2

2x + 3 = 0

### 1.2 Quadratic Equations

Quadratic equations are equations of the type ax^{2} + bx + c = 0, with a ≠ 0.

#### Incomplete quadratic equations

**ax ^{2} = 0**

**ax ^{2} + bx = 0**

**ax ^{2} + c = 0**

### 1.3 Cubic Equations

Cubic equations are equations of the type ax^{3} + bx^{2} + cx + d = 0, with a ≠ 0.

### 1.4 Quartic Equations

Quartic equations are equations of the type ax^{4} + bx^{3} + cx^{2} + dx + e = 0, with a ≠ 0.

#### Biquadratic Equations

Biquadratic equations are quartic equations that do not have terms with an odd degree.

ax^{4} + bx^{2} + c = 0, with a ≠ 0.

## 2. Rational Polynomial Equations

The rational polynomial equations are of the form , where P(x) and Q(x) are polynomials.

## 3. Irrational Polynomial Equations

The irrational equations are those that have at least a polynomial under the radical sign.

## 4. Transcendental Equations

The transcendental equations are equations that include transcendental functions.

### 4.1 Exponential Equations

Exponential equations are equations in which the unknown appears in the exponent.

### 4.2 Logarithmic Equations

Logarithmic equations are equations in which the unknown is affected by a logarithm.

### 4.3 Trigonometric Equations

Trigonometric equations are the equations in which the unknown is affected by a trigonometric function.