1. ## Solve this!

I want to solve this equation for x:

ax^2+cx^(1.5)=b

But this is not as easy as it seemed. Perhaps someone can help.

Gr.
Dirk

2. Originally Posted by dirk_de_groof
I want to solve this equation for x:

ax^2+cx^(1.5)=b

But this is not as easy as it seemed. Perhaps someone can help.

Gr.
Dirk
Hello Dirk
$\displaystyle ax^2+cx\sqrt{x}=b$
$\displaystyle cx\sqrt{x}=b-ax^2$
$\displaystyle c^2x^3=(b-ax^2)^2$ which leads to a fourth degree polynomial equation
I do not know if this is of any help for you

3. ## finding the roots of a 4th degree polynomial

Thank you!
But now I need to find the roots of this 4th degree polynomial.. Does anyone know a method with not too much computational load? The polynomial looks like this:

$\displaystyle au^4+cu^3-b$

Where:
$\displaystyle \sqrt{x}=u$

in:
$\displaystyle ax^2+cx\sqrt{x}-b$

Gr
Dirk

4. There is a method called Ferrari's method but maybe a little bit difficult
Méthode de Ferrari - Wikipédia

Sorry for the French version, I could not find the English one
Anyway mathematics are a universal language !