How to Solve Cubic Equation : ax³+ bx²+ cx+d= 0?

by Alina Jobs Assignment

Learn to Solve Cubic Equations

In mathematical terms, all cubic equations have either one root or three real roots. The general cubic equation is,

ax3+ bx2+ cx+d= 0

The coefficients of a, b, c and d are real or complex numbers with a not equals to zero (a ≠ 0). It must have the term x3 in it, or else it will not be a cubic equation. But any or all of b, c and d can be zero.

The examples of cubic equations are,

No 1, x3+ 3a3+ 3 a2 + a3– b=0

No 2, 4×3+ 57=0

No 3, x3+ 9x=0

Strategy to solve cubic equation

Unlike quadratic equation which may have no real solution; a cubic equation always has at least one real root. The prior strategy of solving a cubic equation is to reduce it to a quadratic equation, and then solve the quadratic by usual means, either by factorizing or using a formula.

Always try to find the solution of cubic equations with the help of the general equation,

ax3+ bx2+ cx+d= 0

A cubic equation should, therefore, must be re-arranged into its standard form,

For example,

x2+ 4x-1 = 6/x

Step 1

You can see the equation is not written in standard form, you need to multiply the ‘x’ to eliminate the fraction and get cubic equation, after doing so, you will end up with

x3+ 4×2– x = 6

Step 2

Then you subtract 6 from both sides in order to get ‘0’ on the right side, so you will come up,

x3+ 4×2– x- 6 = 0

Solving cubic equations with the help of factor theorem

What is factor theorem? If you divide a polynomial p(x) by a factor x — a of that polynomial, then, you will end up with zero as the remainder,

p(x) = (x — a)q(x) + r(x)

If x — a is indeed a factor of p(x), then the remainder after division by x — a will be zero.

p(x) = (x — a)q (x)

Here is a problem,

x3– 5×2– 2x+24 = 0

With x= — 2 a solution.

Factor theorem says that if x = — 2 is a solution of this equation, then x+2 is a factor of this whole expression. So,

x3– 5×2– 2x+24 = 0

can be written in the form,

(x+2)( x2+ ax+b)=0

Where a and b are numbers,

You need to find out what are the values of a and b here by using synthetic division......read more

How MyAssignmentServices.com can help students in maths assignment?

MyAssignmentServices.com has carefully evaluated and assembled a highly-skilled team of in-house experts who are capable of giving the finest maths assignment help you deserve. Your paper will be written by experienced writers in a professional manner. Assignment experts make sure that there are no traces of plagiarism in your content, they only deliver genuine work within the given time limit. If you think sample assignments can help you in your assignment, My Assignment Services offers free samples. Our customer support agents can guide you on how to get free assignments quotes and place your orders.