Irrational equations are equations in which the unknown appears under the sign of a root or is raised to power with a fractional exponent. They are equations of the form:

\[\sqrt[n]{f(x)} = g(x)\]

Rational equations feature at least one fraction in which the numerator and denominator are polynomials. Rational equations have the form:

\[P(x) \over Q(x)\]

Trinomial equations are a specific type of polynomials equations that feature three terms expressed as a combination of variables and constants in the standard form:

\[ ax^{2n} + bx{^2} + c = 0 \]

Binomial equations are a specific type of algebraic equation of the form:

\[a^n x + b = 0\]

Graphically, a quadratic equation in the form \(ax^2 + bx + c = 0\) represents a parabola.

How to avoid the error of root loss in solving second degree equations through the correct interpretation of the variable x.

A quadratic equation is considered incomplete if it lacks one of the terms from the standard form \(ax² + bx + c = 0\), as long as the \(x^2\) term is present.

The most practical and widely used method to solve quadratic equations is by applying the quadratic formula:

\[ x_{1,2} = \frac{{-b \pm \sqrt{{b^2 – 4ac}}}}{{2a}}\]

A quadratic equation, or equation of degree 2, is a second-degree polynomial equation in one variable. The standard form is:

\[ax^2 + bx + c = 0 \quad a \neq 0\]

Linear algebraic equations are algebraic expressions that describe the relationship between variables linearly of the form:

\[a_1x_1 + a_2x_2 + \ldots + a_nx_n = b\]