Trying to find the roots of an n degree polynomial (graphically)

Question

So here we split the equation in 2 parts

Suppose we have an equation $$ax⁴+bx³+cx²+dx+e=0$$ $$\implies bx³+cx²+dx+e= -ax^4$$

Now we plot the graph of LHS and RHS, that is, $bx³+cx²+dx+e$ and $-ax^4$.

The $x$ coordinate of point where these graphs intersect each other is the solution for the given equation.

By this way, we can find the intervals of the solutions by using the techniques of differential calculus.

Following is an example to make the things more clear:

Thanks for reading, have a good day!

Welcome to MSE. It is in your best interest that you type your posts (using MathJax) instead of posting links to pictures. — José Carlos Santos, Jun 20 '22 at 07:43
Why can't we just plot the entire equation at once and see where it hits the $x$-axis? What about complex roots? Also, do you have a question? — Arkady, Jun 20 '22 at 08:51
the purpose of two graph is so that they intersect each other at some point, it later helps in finding the interval, thank you for the suggestion, means a lot — Honey Harshit Srivastava, Jun 20 '22 at 09:47
Welcome to MSE! Here, people ask their questions and the community tries to answer them. In other cases such as yours, the format is to first ask the question and then posting your own solution, this way, the discussion will be more constructive. If your answer/approach is good, it will get upvoted, otherwise you'll see a better approach at the top. The answer that is best according to you, you may "tick-mark" it, this includes your own solution too! — InanimateBeing, Jun 21 '22 at 16:08
https://math.stackexchange.com/questions/4465320/determining-value-for-k-for-minute-and-hour-hand-given-a-condition-in-swapping This is a post where I found a solution to my problem and posted it as an answer, later, I got an even better answer, so I "tick-marked" it. — InanimateBeing, Jun 21 '22 at 17:03

0 Answers0