A quartic equation, also known as a biquadratic equation, is a type of polynomial equation of degree four. It is a special case of a polynomial expression, where the highest power of the variable is raised to the fourth power. The general form of a quartic equation can be represented as:
ax⁴ + bx³ + cx² + dx + e = 0
In this equation, a, b, c, d, and e are constants, and x is the variable. The coefficients a, b, c, d, and e can be any real numbers, except a cannot be zero. If a is zero, the equation is no longer quartic but rather a cubic, quadratic, or linear equation, depending on the degree of the remaining terms.
Solving a quartic equation often requires more complex methods compared to linear, quadratic, or cubic equations. Historically, mathematicians have developed various techniques to solve quartic equations, such as using the factor theorem, substitution, or employing the properties of complex numbers.
Quartic equations can have zero, two, or four real solutions, depending on their discriminant. If the discriminant is positive, there exist two real and two complex non-real solutions. However, if the discriminant is zero, there are two real and two identical solutions. Lastly, if the discriminant is negative, the equation has four complex non-real solutions.
