How To Solve Cubic Equation

How To Solve Cubic Equation?
January 22, 2022

How To Solve Cubic Equation

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The use of the cubic equation solver seems to be one of the latest ways of finding solutions to cubic equations that possibly several students find very difficult to comprehend. The ability to solve higher-order polynomial equations is a necessary skill for anyone pursuing a degree in science or mathematics. Understanding how to solve these types of problems, on the other hand, is complicated.

The moot question on how to solve a cubic equation using several approaches includes:

  • Using dividing technique
  • Theorem
  • The Factor Theorem.
  • Factor using group method used to maximise efficiency.

But first, it is essential to understand what a polynomial and a cubic equation are and then understand the other moves that need to be taken on this issue. Polynomials are algebraic expressions with several terms. Examples of addition and subtraction signs are constant and variable signs. An addition or subtraction sign separates the numerals. An algebraic polynomial has the general form of:

 axn + bxn-1 + cxn-2+ kx + l

where each variable has a constant associated with it, known as its coefficient.

Binomials, trinomials, and quadrinomials are some of the different polynomials that one can find. Polynomials include the following:

3x + 1, x2 + 5xy – axe – 2ay, 6x2 + 3x + 2x + 1, and so on.

What Is a Cubic Equation?

A cubic equation is a third-degree algebraic equation that has three variables.

An equation for a cubic function has the generic form:

f (x)=ax3 + bx2 + cx1 + d.

Also known as the cubic equation, it has the following form: 3abx2 + 3cx + 3d = 0.

The coefficients of the equation are:

3a, 3b, 3c, and 3d, respectively, and the constant is 3d.

How to Solve Cubic Equations?

Traditionally, cubic problems are reduced to quadratic equations and solved using factoring or the quadratic formula. A cubic equation, like a quadratic equation, may have two or three real roots. Unlike quadratic equations, which may or may not have a solution, cubic equations have at least one.

The other two roots are either actual or fictional. So, anytime a cubic or similar equation is supplied, you must first arrange it in a standard form. You will rearrange the numbers and write them as follows:

3x3 + 3x– 2 = 0.

So, if you are given the numbers 3, 2, and 3, you will write it as follows:

3x3 + x2 – 3x – 2 = 0.

Then utilise any method you want to address the problem. Let's look at a couple of instances to understand the process better:

Example No. 1

Calculate the roots of the cubic equation:

2x3 + 3x2 – 11x – 6 = 0 by using a cubic equation solver.


Since d = 6, the factors possibly here are 1, 2, 3, and 6.

Using the Factor Theorem, test the potential values.


f (1) = 2 + 3 + 11 + 6 = 0.

In the negative direction, f (–1) equals the sum of two and three and eleven and six and zero.

f (2) = 16 + 12 – 22 – 6 = 0, and f (3) = 0

As a result, the first root is x = 2.

The synthetic division method can be used to find the other roots of the problem.

The product of:

 (x – 2) (ax2 + bx + c) equals (x – 2) (2x2 + bx + 3) is the product of two variables.

equals (x – 2) (2x2 + 7x + 3) = (x – 2)

(1 – 2) (2x + 1) (x +3) (x +4)

As a result, the result is:

x = 2, x = -1/2, and x = -3.

A free online application, Cubic Equation Solver Calculator, displays the answer to a cubic equation. Because of the online cubic equation solver calculator tool offered, the computation is completed in a fraction of the time, and the result is presented immediately.

What Is a Cubic Equation Calculator? How Does It Work?

The following is the technique to be followed to use the cubic equation solver calculator:

 Step 1. Fill out the appropriate input fields using your equations.

Step 2: To obtain the variable value, press the ‘Answer’ button.

Step 3: The result of the cubic calculation will be displayed in a new window at the end of this step.

What Is Cubic Equation? What Does It Mean?

A cubic polynomial is a polynomial with the maximum degree of three as its highest degree in mathematics. A cubic equation is a type of equation that involves using a cubic polynomial.

All cubic equations have one real root or three real roots. When you solve the cubic equation, you get the following result:



Solve the equation:

 x3-4-2-9x+36=0 by using the distributive property.


We have x3-4-2-9x+36=0 as our result.

In this case, y2 (x-4)-9(x-4) = 0.

the product (x2-9) divided by (x-4) = 0.

= (x-3) (x+3) (x-4) (x-3) (x-4) = 0

In this case, the roots of the following equation are equal to 3, -3, and 4, respectively.

Understanding the cubic equation needs rigorous practising of the various assignments. It can at best do with the help of online assignment helpers providing mathematical methods for assignment help.

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4) Insufficient practice which leads to disinterest:

Lack of sufficient practice is the root cause for disinterest in the subject. Most of the time a student, when left alone to solve an equation with cubic equation solvers is unable to do so. Lack of sufficient practice is one of the reasons for the inability. Mathematics, requires a great deal of effort and patience! As tutors, the councillors make a concerted effort to pinpoint the specific areas where students need to improve, helping them close their learning gaps.

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