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
Quadratic equations are equations of the type ax2 + bx + c = 0, with a ≠ 0.
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 are quartic equations that do not have terms with an odd degree.
ax4 + bx2 + c = 0, with a ≠ 0.
The rational polynomial equations are of the form , where P(x) and Q(x) are polynomials.
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.
Exponential equations are equations in which the unknown appears in the exponent.
Logarithmic equations are equations in which the unknown is affected by a logarithm.
Trigonometric equations are the equations in which the unknown is affected by a trigonometric function.