16 results for
polynomials
algebrica.org > rational-equations

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

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

algebrica.org > binomial-equations

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

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

algebrica.org > geometrical-meaning-quadratic-equations

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

algebrica.org > loss-of-roots

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

algebrica.org > incomplete-quadratic-equations

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.

algebrica.org > factoring-quadratic-equations

Method to break down an equation into a product of binomials, facilitating the solution and analysis of its roots and graphs.

algebrica.org > quadratic-formula

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

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

algebrica.org > quadratic-equations

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

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

algebrica.org > ruffinis-rule

Ruffini’s rule provides a systematic and efficient method for polynomial division, which leads to a rapid factorization of polynomials and the solution of equations of degree \(n > 2\).

algebrica.org > notable-products

Particular products of powers, binomials, and trinomials are known as notable products.