What is a Cubic Equation? - Definition & Examples

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  • 0:01 Examples
  • 2:01 More Examples
  • 2:32 In Algebra
  • 3:09 In Real Life
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In algebra, you come across various kinds of functions. You start learning about linear functions, and then quadratic functions. Now, though, you come across cubic functions. What are they? Watch this video lesson to find out.

Examples of Cubic Equations

As you progress in your studies of algebra, you are exposed to more and more types of equations. You now are familiar with linear and quadratic equations. You know what they are and you can identify them easily. You can even tell a friend why they are important to know.

Now that you know both linear and quadratic equations like the back of your hand, it is now time to learn about cubic equations. What are they? Why are they important in life? Keep watching this video lesson, and we will find out!

First off, cubic equations are equations with a degree of 3. This means that the highest exponent is always 3. In algebra, we can write their general form as ax^3 + bx^2 + cx + d = 0, where a, b, c, and d are numbers, with the one restriction that a cannot be 0. So, cubic equations can have just one term as long as it has an exponent of 3.

It can also have up to four terms. For example, 4x^3 = 0 is a cubic equation, as is 4x^3 + 3x^2 + 2x + 1 = 0. Notice that both of these cubic equations have that little 3 as the highest exponent. It is this little 3 that you will always look for when you want to identify a cubic equation.

The equation x + 2x^3 + x^2 = 0 is also a cubic. Notice the little 3 that is our highest exponent. This equation just happens to be written out of order. We can rewrite it in the standard form by writing the x^3 term first, followed by the x^2, and so on. Rewriting it, we get 2x^3 + x^2 + x = 0.

More Examples of Cubic Equations

Cubic equations come in all sorts. All of these are examples of cubic equations:

  • x^3 = 0
  • 2x^3 + 4x + 1 = 0
  • 4x^3 + x^2 + 4x - 8 = 0

Do you see that all of these have the little 3? Just remember that for cubic equations, that little 3 is the defining aspect. Now, let's talk about why cubic equations are important.

Cubic Equations in Algebra

In algebra, cubic equations have been around for centuries. The ancient Babylonians had ways of calculating cubic equations. Archeologists have found really old Babylonian tablets that showed tables that helped people back then to solve cubic equations. This goes all the way back to the 20th century BC. Now that's really old! Since then, mathematicians over time have added to the knowledge of solving cubic equations. We now have several methods to solve them thanks to all the hard work of mathematicians over the years.

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