Quartic equation root calculator

For example, input：a=3, b=6, c=-123, d=-126 e=1080
ax4 + bx3 + cx2 + dx + e = 0
x4 + x³ + x² + x + e
Results:
x1: +   i
x2: +   i
x3: +   i
x4: +   i

A Quartic Equation Root Calculator is a tool used to find the roots (solutions) of a quartic equation, which is a polynomial equation of degree 4.

What is a Quartic Equation?

A quartic equation has the general form:

where a,b,c,d,e are real or complex numbers, and a≠0.

Why Use a Quartic Equation Root Calculator?

  • Manually solving quartic equations is complex and time-consuming.
  • The formula for quartic equations is long and difficult to apply without errors.
  • It helps in engineering, physics, algebra, and calculus problems where quartic equations arise.

How Does It Work?

A quartic equation root calculator typically:

  1. Accepts coefficients a,b,c,d,e as input.
  2. Uses the Ferrari’s method or numerical approximations to find the roots.
  3. Outputs the real and complex roots of the equation.

When Is It Used?

  • When solving higher-degree polynomial equations in algebra.
  • In physics and engineering for modeling waveforms, mechanical vibrations, and optics.
  • In finance and economics for solving equations related to interest rates and investments.