I am able to solve equation x^3 + 3x^2 + 3x + 1 = 0 using Mathematica by using the command
Solve[x^3 + 3x^2 + 3x + 1 == 0, x]
But not able to solve ax^3 + bx^2 + cx + d = 0 for general variables a,b,c,d using Mathematica.
Can anyone suggest me how this or any general polynomial equation of any degree could be solved using Mathematica.
Once you get up to third order polynomials, the solutions depend on the coefficients. That is, different coefficients require different approaches or formulas. You can always solve polynomials numerically. This works quite well for real and complex roots. You can use Newton-Raphson or several other methods. Mathematica and several other tools will graph the polynomial so that you can visualize the behavior over a given domain. You can do a 2D plot for complex values.
Just tried it and there didn’t seem to be any such problem, though the expressions, of course, are unwieldy.
Your true question is about finding the roots of the general polynomial equation of any degree using Mathematica. According to Abel–Ruffini theorem, there is no solution in radicals to general polynomial equations of degree five or higher with arbitrary coefficients.
Thus, for general polynomials, I suggest that you use the Roots[lhs == rhs, var] command, if the coefficients are known.
https://reference.wolfram.com/language/ref/Roots.html
For the cubic, which is bring discussed here, ecpressions for arbitrary values of the coefficients can be found; they’re, just, unwieldy to use in practice, which is why they aren’t.
- Badges
- Science topic
- Similar topics
- Linguistics
- Composition Studies
- Writing