MHB Solving \[x^{4}-4x^{3}+10=0\] with a "Binary Search

[Yankel]

Hello all

I am trying to draw a graph of a function. On the way, I wanted to see where the function meet the x axis, so I put y=0. It gave me this:

\[x^{4}-4x^{3}+10=0\]

How do I solve this equation ?

Thanks !

I tried a "binary search" and got really close to the answer, but I guess there must be a better way...

 

[SuperSonic4]

Hello all

I am trying to draw a graph of a function. On the way, I wanted to see where the function meet the x axis, so I put y=0. It gave me this:

\[x^{4}-4x^{3}+10=0\]

How do I solve this equation ?

Thanks !

I tried a "binary search" and got really close to the answer, but I guess there must be a better way...

It's not easy...
Quartic function - Wikipedia, the free encyclopedia

A binary search or goal seek in excel are probably your best bets with a numerical approximation being next. Honestly this is one of those questions I'd just put into wolfram and use their answer(s)

 

[topsquark]

Hello all

I am trying to draw a graph of a function. On the way, I wanted to see where the function meet the x axis, so I put y=0. It gave me this:

\[x^{4}-4x^{3}+10=0\]

How do I solve this equation ?

Thanks !

I tried a "binary search" and got really close to the answer, but I guess there must be a better way...

You can occasionally use the rational root theorem, but it doesn't work for this equation.

-Dan

 

[Yankel]

I understand, thank you !

What numerical approximation methods do we have to solve such equations ?

 

[MarkFL]

I understand, thank you !

What numerical approximation methods do we have to solve such equations ?

Perhaps the best known is:

Newton's Method