# How to solve a quadratic which has a term with a square root over the variable?

• Dec 7th 2013, 02:24 AM
AaPa
How to solve a quadratic which has a term with a square root over the variable?
How to solve a quadratic which has a term with a square root over the variable?
• Dec 7th 2013, 02:31 AM
chiro
Re: How to solve a quadratic which has a term with a square root over the variable?
Hey AaPa.

Can you show us what equation/expression/function you are talking about?
• Dec 7th 2013, 03:53 AM
AaPa
Re: How to solve a quadratic which has a term with a square root over the variable?
like

x^2+2x+3+4(sqrt(x))=0
• Dec 7th 2013, 05:29 AM
Soroban
Re: How to solve a quadratic which has a term with a square root over the variable?
Hello, AaPa!

Quote:

How to solve: . $x^2+2x+3+4\sqrt{x} \:=\:0$

This is not a quadratic.

You have: . $x^2 + 2x + 4\sqrt{x} + 3 \:=\:0$

Let $\sqrt{x}=u \quad\Rightarrow\quad x = u^2$

The equation becomes: . $u^4 + 2u^2 + 4u + 3 \:=\:0$

And you have a quartic to solve.
• Dec 7th 2013, 05:35 AM
AaPa
Re: How to solve a quadratic which has a term with a square root over the variable?
Thanks.