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?

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?

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

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

Hello, AaPa!

Quote:

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

This is *not* a quadratic.

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

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

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

And you have a *quartic* to solve.

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