Why the roots of Eq. x^2 + a*x + b = 0 and of Eq. x + a*Sqrt[x] + b =

[Lucasss84]

Why the roots of Eq. x^2 + a*x + b = 0 and of Eq. x + a*Sqrt[x] + b = 0 are not identically? How can I expand the second Eq. in simple fractions: x + a*Sqrt[x] + b = ... ?
Thank you. Lucas

 

[micromass]

Why the roots of Eq. x^2 + a*x + b = 0 and of Eq. x + a*Sqrt[x] + b = 0 are not identically?

Why would they be identical? They are different equations, so I see no reason why they should be identical.

How can I expand the second Eq. in simple fractions: x + a*Sqrt[x] + b = ... ?

What do you mean with "simple fractions"??

Do you mean that you want to factor it? Well, first you need to find the roots, you can do that by substituting $y=\sqrt{x}$.
Once you found the roots $\xi_1,\xi_2$, then we can factor

$$(\sqrt{x}-\xi_1)(\sqrt{x}-\xi_2)$$

 

[crocque]

I'm no mathmetician, but seems like you don't really need a number, just a variable. Look up the imaginary number i. Wish I was more educated.