Easy Tips To Solve Cubic Equations
How To Solve Cubic Equation: Ax3+Bx2+Cx+D=0
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 stepwise so that the roots become crystal clear to you.
How can I solve a cubic equation in one variable?
Examples

4x3+2x211x+12=0

13x33x298=0

34x3+76x229x=0

2x3+23x2=0
The Solving Tips
Example: x35x22x+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:
X35x22x+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 2 242 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: x27x+12=0. It would be reduced to the form – (x+2)(x27x+12)=0
Step 8
By solving the quadratic equation by factorisation method, we will get – (x+2)(x3)(x4) = 0. Therefore the roots of x35x22x+24 + 0

x=2

x= 3

x=4