Solving Polynomial Equations 4: The pattern with the cubic case | Explore Research Maths | Wild Egg

We begin a careful look at our simplest power series solution to the general cubic equation. Which terms appear? What are the signs in front of them? And what are the coefficients that come with them? These are little puzzles that we must solve to make progress on the bigger problem of finding a general solution.

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[moustafashahin]

thank you Prof.Wildberger for these lectures. I am not a mathematician but I love mathematics. I really liked the video series about math history. Recently I knew about Pell’s equation and I think I found interesting thing about solvability of Generalized pell's equation it will kind of if you have a look at it

[danielmilyutin]

`Index degree` follows from (physical) dimension theory.
c0, c1*x, c2*x^2 etc. must all have same physical dimension.

[relikep]

Is there a way to approximate all three roots of the equation?

[accountname]

as we increase k, do the coefficients of the c_j terms when decomposed into their primes, ever contain a prime whose index in the collection of primes is greater than k?
Oh nice by the end you're addressing this. I shall play around some more and look forward to your solution later.
Great content as always norm!