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

1. Aug 9, 2011

### 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

2. Aug 9, 2011

### micromass

Re: Roots

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

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

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

3. Aug 14, 2011

### crocque

Re: Roots

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.