1. ## Finding real solutions

For what values of c does the following equation have at least one real solution?

$\displaystyle cx^2+sqrt(c) x = c$

2. ## Re: Finding real solutions

Originally Posted by Saphira
For what values of c does the following equation have at least one real solution?
$\displaystyle cx^2+\sqrt{c}x=c$
You want $\displaystyle (\sqrt{c})^2-4(c)(-c)\ge0$

3. ## Re: Finding real solutions

Are we assuming $\displaystyle c \ne 0$?

Are we assuming $\displaystyle c \in \mathbb{R}$?

4. ## Re: Finding real solutions

The value of c is not specified, so I'm guessing, yes.

5. ## Re: Finding real solutions

Originally Posted by Plato
You want $\displaystyle (\sqrt{c})^2-4(c)(-c)\ge0$
Thanks!

6. ## Re: Finding real solutions

Okay, have you considered the Quadratic Formula and the implications of the radical?

7. ## Re: Finding real solutions

Originally Posted by Saphira
For what values of c does the following equation have at least one real solution?

$\displaystyle cx^2+sqrt(c) x = c$
1. c is positive since otherwise $\displaystyle \sqrt{c}$ is not real and I presume we want it to be real.

2. Rewrite the equation:

$\displaystyle cx^2+\sqrt{c}x-c=0$

What does Descartes rule of signs tell you when $\displaystyle c>0$.

CB