Check Out The Easiest Method Of Solving Cubic Equation using Tartaglia's Formula

I don't understand mathematics, I hate it, I can't know Mathematics, it is just confusing

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Mathematics has been a subject or course causing creating lot of problems to students and other people. Some people tend to give up on mathematical problems due to it's strenuous nature and the inability to apply cognitive skills.
This has caused large amount of students disliking Mathematics. Some got discouraged because they were deceived by their friends with the mindset Mathematics is difficult.

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But This Is All What Mathematics Is All About

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Mathematics is all about understanding and application of mathematical principle to solve mathematical problems. A Mathematical scholar once said "The best way to know Mathematics is to do Mathematics"
You just have to keep solving more mathematical problems and never give up easily. Stay focused and avoid the mindset I can't know mathematics. You are a Genius with hidden power but you never wana show it because you are afraid of failing, or you got distracted by what others are saying.

The Cubic Equation or Cubic Function

It's time to let the cat out of the bag😊. The Cubic function is identified based on the highest value of the variable which is 3.
Cubic literally means 3 to a layman because it is derived from cube. This means cubic function usually have 3 has it's highest power.

Examples of cubic function involves

• f(x)=ax³ +bx² +Cx +d

• x³ +5x² +6x +7=0

• x³ +5x +2

• x³ +7=0

• x³ +3x² +4=0

It is observed from the above examples that the highest power of "x" is 3. This makes it a cubic equation.It is expected to get 3 solutions from cubic equations after solving, such values may yield real value, complex or irrational values.

*Based on my little research I was able to conclude that:

"The highest power of the variable will determine the number of solutions."

This literally means if the highest power of the equation is 2(as we have in quadratic equation), it will yield two solutions. Similarly, if the highest power is 3(as we have in Cubic Equation) it will yield 3 solutions and so on.
Thus, this is illustrated below:

• ax^n +bx^(n-1) +bx^(n-2)...... =0 =>n solutions

• 3x^5 +5x⁴ + 2x³ +7x² +8x +9=0 =>5 solutions

• 2x⁴ +3x³ + 6x² - 5x +4=0 => 4 solutions

• 10x³ +2x² +6x +5=0 =>3 solutions

• 6x² +5x +4=0 => 2 solutions

• 9x +5=0 => 1 solution

Before I continue, I will explain a slight difference between equation and expression.

A function becomes an equation when it is equated to a value and it is becomes expression when it is not equated to anything.

Example of an equation is given by

• 3x²+5x=0

• 4x² +9x +8=0

• 8x³ +4x² +7=0

An Example of an expression is given by

• 6x+4

• (5x+4)(3x+2)

• (x² +3)(x+4)

Applying Tartaglia's Formula To Solve Linear Cubic Equations.

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Just as we solve Quadratic Equation using either Factorization, completing the square method or Formula method, we can apply Tartaglia's Formula to solve Cubic Equation. You can read more about Quadratic Equation via [https://steemit.com/mathematics/@hardaeborla/quadraticequation].

The Tartaglia's Formula is given by

Let now solve a Cubic Equation 😀

• Example : Find a real solution for x in the equation x³ +6x² - 4x +5=0

STEP 1: Reduce in the form x³ +ax +b=0

This is achieved by putting x=y -( 6/3)
Thus, x=y-2.
Substitute y-2 for x in the Cubic Equation

x³ +6x² - 4x +5=0
(y-2)³ +6(y-2)-4(y-2)+5=0
Expanding Using Binomial Expansion (Pascal Triangle), we have

[y³ - 3y²(2) +3y(4) - 8]+6[y² - 4y +4] - 4(y-2) +5=0

y³ - 6y² +12y - 8 - 6y²-24y +24-4y +8=0

y³ - 16y +29=0

Step 2: Apply Tartaglia's Formula

Before using Tartaglia's Formula, a>0. But in this case we can notice a<0 =(-16). We multiple through by - 1. We now have:

-y³ +16y - 29=0

We apply Tartaglia's Formula where a=16 and b=-29

y=(-b/2 +√((a/3)³ + (b/2)²)^(1/3)+(-b/2-√((a/3)³ + (b/2)²)^(1/3)

Substitute for "a" and "b" to yield a value after solving which gives y= - 4. 705

Step 3: Get the value of x using the relationship between "x and y"

For this question, recall that x=y-2

Input your value for "y" from step 2. This implies that :

x=y-2

Recall that x= - 4.705

x= - 4.705 - 2

x= -6.705

I was able to get a real value of the Cubic Equation by Tartaglia's Formula. We can get the two values by following the below steps.

• Divide the Cubic Equation by (x+6.705). It is "+" because the factor is negative. Apply the reverse when the factor is positive.

• After dividing, you will surely obtain a Quadratic Equation.

• Solve the Quadratic Equation either by Factorization, completing the square or Formula Method. I recommend you make use of Formula Method for better accuracy.

Thank you for your time. Follow me @Hardaeborla for more Enticing posts and don't forget to #upvote or #like if you found this helpful