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 = x2 - 2

x2 + 2x + 1 = x2 - 2

2x + 1 = -2

2x + 3 = 0

1.2 Quadratic Equations

Quadratic equations are equations of the type ax2 + bx + c = 0, with a ≠ 0.

Incomplete quadratic equations

ax2 = 0

ax2 + bx = 0

ax2 + c = 0

1.3 Cubic Equations

Cubic equations are equations of the type ax3 + bx2 + cx + d = 0, with a ≠ 0.

1.4 Quartic Equations

Quartic equations are equations of the type ax4 + bx3 + cx2 + dx + e = 0, with a ≠ 0.

Biquadratic Equations

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

ax4 + bx2 + c = 0, with a ≠ 0.

2. Rational Polynomial Equations

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

Rational Polynomial Equations

3. Irrational Polynomial Equations

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

Irrational Polynomial Equations

Irrational Polynomial Equations

Irrational Polynomial Equations

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.

Exponential Equations

Exponential Equations

Exponential Equations

4.2 Logarithmic Equations

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

Logarithmic Equations

Logarithmic Equations

Logarithmic Equations

4.3 Trigonometric Equations

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

Trigonometric Equations

Trigonometric Equations

Trigonometric Equations