4th Degree Equation Calculator

The 4th Degree Equation Calculator, also known as a Quartic Equation Calculator allows you to calculate the roots of a fourth-degree equation. This page includes an online 4th degree equation calculator that you can use from your mobile, device, desktop or tablet and also includes a supporting guide and instructions on how to use the calculator.

Quartic Equation Calculator
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Quartic Equation Calculator Results
x1: +i
x2: +i
x3: +i
x4: +i

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How is this calculator useful for me?

The 4th Degree Equation calculator Is an online math calculator developed by calculator to support with the development of your mathematical knowledge. You can use it to help check homework questions and support your calculations of fourth-degree equations. This is particularly useful if you are new to fourth-degree equations or need to refresh your math knowledge as the 4th degree equation calculator will accurately compute the calculation so you can check your own manual math calculations.

How to calculate the root of the fourth degree?

You can calculate the root of the fourth degree manually using the fourth degree equation below or you can use the fourth degree equation calculator and save yourself the time and hassle of calculating the math manually. You can also use the calculator to check your own manual math calculations to ensure your computations are correct and allow you to check any errors in your fourth degree equation calculation(s).

Quartic Equation Formula:

ax4+ bx3 + cx2 + dx + e = 0
p = sqrt(y1)
q = sqrt(y3)7
r = - g /(8pq)
s = b /(4a)
x1 = p + q + r - s
x2 = p - q - r - s
x3 = -p + q - r - s
x4 = -p - q + r - s

How to calculate the root of the fourth degree using the 4th degree equation calculator?

For those who already know how to caluclate the Quartic Equation and want to save time or check their results, you can use the Quartic Equation Calculator by following the steps below:

  1. Enter a value for ax4
  2. Enter a value for xb3
  3. Enter a value for cx2
  4. Enter a value for dx
  5. Enter a value for e
  6. The 4th Degree Equation Calculator will calculate the roots of the 4th degree equation you have entered

History behind the 4th degree equation

The Quartic Equation formula was first discovered by Lodovico Ferrari in 1540 all though it was claimed that in 1486 a Spanish mathematician was allegedly told by Tomás de Torquemada, a Chief inquisitor of the Spanish Inquisition, that "it was the will of god that such a solution should be inaccessible to human understanding" which resulted in the mathematician being burned at the stake.

Despite Lodovico discovering the solution to the quartic in 1540, it wasn't published until 1545 as the solution also required the solution of a cubic which was discovered and published alongside the quartic solution by Lodovico's mentor Gerolamo Cardano within the book Ars Magna.

How does this formula apply within life?

Quartic equations are actually quite common within computational geometry, being used in areas such as computer graphics, optics, design and manufacturing. They can also be useful for calculating ratios.

For example within computer aided manufacturing the endmill cutter if often associated with the torus shape which requires the quartic solution in order to calculate its location relative to a triangulated surface.