Easy Tips To Solve Cubic Equations
20-Jan-2023 12:11 PM
How To Solve Cubic Equation: Ax3+Bx2+Cx+D=0
Any maths student here? Are you stuck with your math homework in solving cubic equations? Well, there is a huge difference between high-school mathematics and university-level mathematics. It becomes embarrassing if you are not able to solve a question at the high school level in college. The basic concepts are required to be clear for attempting any numerical question.
As it is a widely known fact that mathematics and students are opposite poles. If you are here then it is evident that you are also facing problems in solving the cubic equations of algebra. Math assignment help is just the right place for you to take assistance from. They have the best math experts who will explain everything step-wise so that the roots become crystal clear to you.
As it is a widely known fact that mathematics and students are opposite poles. If you are here then it is evident that you are also facing problems in solving the cubic equations of algebra. Math assignment help is just the right place for you to take assistance from. They have the best math experts who will explain everything step-wise so that the roots become crystal clear to you.
How can I solve a cubic equation in one variable?
The terms of mathematics can be tricky. Particularly, the cubic equations seem confusing as there are plenty of solutions for the variable x. Every equation has a number of values for x which is known as the roots. The number of real roots depends on the power of the variable. The general cubic equation is ax3+bx2+cx+d=0. The letters a, b, c, and d are the coefficients. The coefficients can be a complex number or a real number, where the value of ‘a’ is not equal to zero. If you are wondering why the answer is pretty simple. The equation needs an x3 term so it is called a cubic equation. Apart from ‘a, any other coefficient can be zero.
Examples
-
4x3+2x2-11x+12=0
-
13x3-3x2-98=0
-
34x3+76x2-29x=0
-
2x3+23x2=0
The Solving Tips
There is another type of equation, the quadratic equation. The quadratic equation is not bound to have an equal root. The cubic equations have at least one real root. It is always better to jot down a cubic equation to a quadratic equation, if possible, as the latter has a maximum power of 2. The solving of a square-powered equation becomes easy and less complicated. Let us take one example so that the process is understood clearly.
Example: x3-5x2-2x+24=0
Let us consider that x= -2 is the sure solution of the above equation. Thus, according to the factor theorem, (x+2) is the factor of the above example. Hence, it can be written as the following:
X3-5x2-2x+24=0 implies as - (x+2)(x2+ax+b)=0,
The values of ‘a’ and ‘b’ are required to be found with the help of the synthetic division method.
Step 1
The coefficients of the original cubic equation are 1, -5,-2 and 24
1 -5 -2 24
x= -2
1
Step 2
You need to multiply the number (1) that is brought down by a known root -2. As the supposed result is -2, it is mentioned in the other line
1 -5 -2 24 -2
x= -2
1
Step 3
Adding the number in the second column
1 -5 -2 24 -2
x= -2
1 -7
Step 4
Multiply the sum with the known root that is -7 which is multiplied by -2. The answer is shown in the second row.
1 -5 -2 24 -2 14
x= -2
1 -7
Step 5
Adding the number in the third column
1 -5 -2 24-2 14 -24
x=-2
1 -7 12
Step 6
Repeat the multiplication process, we will get 12 multiplied by -2
1 -5 -2 24 -2 14 -24
x=-2
1 -7 12
Adding the number in the final column will get a result of the following
1 -5 -2 24 -2 14 -24
x=-2
1 -7 12 0
Step 7
Now, after getting 0 as the final coefficient, it has become sure that -2 s the ultimate root of the equation. The last row of step seven can form a quadratic equation: -x2-7x+12=0. It would be reduced to the form – (x+2)(x2-7x+12)=0
Step 8
By solving the quadratic equation by factorisation method, we will get – (x+2)(x-3)(x-4) = 0. Therefore the roots of x3-5x2-2x+24 + 0
Example: x3-5x2-2x+24=0
Let us consider that x= -2 is the sure solution of the above equation. Thus, according to the factor theorem, (x+2) is the factor of the above example. Hence, it can be written as the following:
X3-5x2-2x+24=0 implies as - (x+2)(x2+ax+b)=0,
The values of ‘a’ and ‘b’ are required to be found with the help of the synthetic division method.
Step 1
The coefficients of the original cubic equation are 1, -5,-2 and 24
1 -5 -2 24
x= -2
1
Step 2
You need to multiply the number (1) that is brought down by a known root -2. As the supposed result is -2, it is mentioned in the other line
1 -5 -2 24 -2
x= -2
1
Step 3
Adding the number in the second column
1 -5 -2 24 -2
x= -2
1 -7
Step 4
Multiply the sum with the known root that is -7 which is multiplied by -2. The answer is shown in the second row.
1 -5 -2 24 -2 14
x= -2
1 -7
Step 5
Adding the number in the third column
1 -5 -2 24-2 14 -24
x=-2
1 -7 12
Step 6
Repeat the multiplication process, we will get 12 multiplied by -2
1 -5 -2 24 -2 14 -24
x=-2
1 -7 12
Adding the number in the final column will get a result of the following
1 -5 -2 24 -2 14 -24
x=-2
1 -7 12 0
Step 7
Now, after getting 0 as the final coefficient, it has become sure that -2 s the ultimate root of the equation. The last row of step seven can form a quadratic equation: -x2-7x+12=0. It would be reduced to the form – (x+2)(x2-7x+12)=0
Step 8
By solving the quadratic equation by factorisation method, we will get – (x+2)(x-3)(x-4) = 0. Therefore the roots of x3-5x2-2x+24 + 0
-
x=-2
-
x= 3
-
x=4
Need Assistance With Math Assignments?
I hope with the above example, the solving of the cubic equations must have become clear to you. You can always take help from math assignment help services. The math experts are highly qualified and experienced. They will deliver the correct solution to you. They can also tutor you on your demand. They can also add explanations to the steps just like I did so that every step is clear to you.
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