Solve using quadratic formula?

You have two quadratic equations. Both equations are the same.In summary, the conversation is about struggling to solve a system of equations to find values for θ1 and θ2. The equations are symmetric and result in a quadratic equation for both θ1 and θ2. The speaker is asking for help in finding the correct solutions.
  • #1
Kinetica
88
0

Homework Statement



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

θ12
θ12

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.
 
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  • #2
Kinetica said:

Homework Statement



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

θ12
θ12

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.
 
  • #3
Kinetica said:

Homework Statement



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

θ12
θ12

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
 
  • #4
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.
 

FAQ: Solve using quadratic formula?

What is the quadratic formula?

The quadratic formula is an equation used to find the solutions or roots of a quadratic equation, which is an equation in the form of ax^2 + bx + c = 0.

When should the quadratic formula be used?

The quadratic formula should be used when solving a quadratic equation that cannot be easily factored or when there are no real solutions.

What are the parts of the quadratic formula?

The parts of the quadratic formula are a, b, and c, which represent the coefficients of the quadratic equation in the form of ax^2 + bx + c = 0.

How do you use the quadratic formula to solve an equation?

To solve an equation using the quadratic formula, substitute the values of a, b, and c into the formula and simplify to find the solutions or roots of the equation.

Are there any restrictions when using the quadratic formula?

Yes, the quadratic formula can only be used to solve quadratic equations. It cannot be used for linear or higher degree equations.

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