Solve using quadratic formula?

[Kinetica]

Homework Statement

Hey guys, recently, I struggled to solve this equation.
I need to find θ₁ and θ₂ by using this system of equations:

θ₁+θ₂=γ
θ₁*θ₂=β

After letting θ₂=β/θ₁, I plugged this into the first equation. I got:

θ₁²-γθ₁+β=0

At this point I get a very unsexy θ₁ result by using quadratic solution.

Need you help!

P.S. This way, I get 4 solutions overall, but my professor is saying that there should only be 2 solutions.

 

[Dick]

Homework Statement

Hey guys, recently, I struggled to solve this equation.
I need to find θ₁ and θ₂ by using this system of equations:

θ₁+θ₂=γ
θ₁*θ₂=β

After letting θ₂=β/θ₁, I plugged this into the first equation. I got:

θ₁²-γθ₁+β=0

At this point I get a very unsexy θ₁ result by using quadratic solution.

Need you help!

What you've done so far is just fine. And I don't think the answer is going to pretty no matter how you do it.

 

[Ray Vickson]

Homework Statement

Hey guys, recently, I struggled to solve this equation.
I need to find θ₁ and θ₂ by using this system of equations:

θ₁+θ₂=γ
θ₁*θ₂=β

After letting θ₂=β/θ₁, I plugged this into the first equation. I got:

θ₁²-γθ₁+β=0

At this point I get a very unsexy θ₁ result by using quadratic solution.

Need you help!

P.S. This way, I get 4 solutions overall, but my professor is saying that there should only be 2 solutions.

How did you get 4 solutions? Could you show us? The point is that you must have made an error, and we cannot help until we know what you did.

RGV

 

[epenguin]

If you look at your equations they are symmetric between θ₁ and θ₂. You could say there is no difference between θ₁ and θ₂. Or, do what you did to get a quadratic equation for θ₁ but do it to get an equation for θ₂ instead - you find you have got exactly the same equation for θ₂ as you got for θ₁.

You haven't really got two quadratic equations, you've got one.