CUBIC EQUATION Meaning and
Definition
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A cubic equation is a type of polynomial equation of degree 3, which is an algebraic equation containing a variable raised to the power of 3. It can be defined as an equation that can be rearranged in the form ax^3 + bx^2 + cx + d = 0, where a, b, c, and d are coefficients and x is the unknown variable.
The cubic equation derives its name from the fact that the highest power of the variable is 3, resulting in a cubic curve when graphed. The equation may possess one, two, or three real roots, which are the values of x that satisfy the equation, and may also have complex roots.
Solving a cubic equation can be a complex process and often requires the application of mathematical techniques such as factoring, synthetic division, or the use of special formulas like Cardano's formula or Vieta's formulas. Additionally, the fundamental theorem of algebra states that every cubic equation has at least one real root or one real root and a pair of complex conjugate roots.
Cubic equations find applications in various fields of science, engineering, and mathematics, particularly in modeling physical phenomena, solving optimization problems, or determining solutions for equations with multiple unknowns.
In summary, a cubic equation is a type of polynomial equation in which the highest power of the variable is 3 and can be expressed as ax^3 + bx^2 + cx + d = 0, possessing one to three real or complex roots.
Etymology of CUBIC EQUATION
The word "cubic" refers to a polynomial equation of degree three, where the highest exponent of the variable is three. The term "cubic" is derived from the Latin word "cubicus", which means "cubical" or "related to a cube". This is because when graphed, a cubic equation often forms a shape resembling a cube. The usage of the term "cubic equation" can be attributed to its geometric connection with cubes.
