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3 Different Ways to Solve Cubic Equations Easily

24 Jan 2020 44201 5 minutes
How to Solve a Cubic Equation Problem?

3 Different Ways to Solve Cubic Equations Easily

When you are assigned with a cubic equation problem in your assignment by your maths professor, then it may look unsolvable for you in the beginning. However, the easy ways for solving it has been already introduced hundreds of years ago. We know that finding the solution is a bit difficult, but with the right approach, even the most complex and trickiest cubic equation can be solved easily. Here are a few strategies to tackle with it.

Way 1: Solve It with Quadratic Formula

Cubic equation are in the form of ax3+bx2+cx+d=0

If you see that the equation is not in standard form, then do the basic arithmetic calculations to get the cubic equation.

On the other hand, if the equation contains a constant, then you need to follow a different approach.

Divide the Equation with an X

Since your equation has an X variable in it, one X can be factored out in the form of:


Use the Quadratic Formula to Solve it

The obtained equation is in quadratic form. This means that now you can easily find the values of a, b, and c just by placing them in the quadratic formula, i.e.,


Way 2: Finding Solutions with Integers

The way maintained above is quite convenient because you don't have to implement any new mathematical formula or trick. But, it won't help you with all the cubic equations.  
Like, if your equation has a non-zero value for d, then you need to follow the step mentioned below.

Example: 2x3+5x2+15x+6=0

In this the value of d is 6, so you can't implement the above method.

Here you have to find the factors of a and d

D=6=6*1, 3*2

Factors of a=1,2 and of d=1,2,3,6.

Divide the factors of a by d
The next step is to make a list of the values that you get after dividing each factor of a by each factor of d.

1,1/2,1/3,1/6 and 2,1,2/3,3

Next, add the negatives to it

-1,-1/2,-1/3,-1/6 and -2,-1,-2/3,-3

Check Your Answers Manually

Once you have got the list of the values, you can easily find the answers to your cubic equation quickly by plugging each integer manually and finding which one equals zero. However, if you don't want to calculate the answers by this method, then you can go with another technique called synthetic division.

Way 3: Follow a Discriminant Approach

For this method of finding a cubical equation solution, you have to deal with the coefficients of the terms in the equation.

For example: if your equation is x3-3x2+3x-1, we would write a=1, b=-3, c=3, and d=1. Don't forget that when a variable doesn't have a coefficient, it's implicitly assumed that its coefficient is 1.

So, these are the three different ways to solve a cubic equation easily. Well, solving maths assignments require too much efforts and patience. And, if because of your extracurricular activities you don't have enough time to complete them, then you can opt for our online assignment help service.

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