Without solving the equation, find the value of the roots

  • Thread starter Thread starter BOAS
  • Start date Start date
  • Tags Tags
    Roots Value
AI Thread Summary
The discussion revolves around finding the value of (\alpha - \beta)^2 from the quadratic equation 23 - 5x - 4x^2 = 0. The user has previously calculated \alpha + \beta and \alpha\beta but is unsure how to proceed. A key insight provided is that (\alpha - \beta)^2 can be expressed as (\alpha + \beta)^2 - 4\alpha\beta. This formula allows the user to utilize their earlier calculations to find the desired value. The conversation concludes with the user expressing gratitude for the helpful nudge in the right direction.
BOAS
Messages
546
Reaction score
19

Homework Statement



23 - 5x - 4x2 = 0

find (\alpha - \beta)2



Homework Equations



In previous parts of the question I've calculated \alpha + \beta, \alpha\beta, 1/\alpha + 1/\beta and (\alpha+1)(\beta+1) but I can't think of any rules I know to help me solve the problem.

The Attempt at a Solution



Expanding (\alpha - \beta)2

gives

\alpha2+\beta2 -2\alpha\beta

But I don't know what I can do with this info.

I'd appreciate a nudge in the right direction!

Thanks
 
Physics news on Phys.org
You can write your expression fairly simply in terms of \alpha+\beta and \alpha \beta (from which you can get the final answer according to your part 2)
 
BOAS said:

Homework Statement



23 - 5x - 4x2 = 0

find (\alpha - \beta)2



Homework Equations



In previous parts of the question I've calculated \alpha + \beta, \alpha\beta, 1/\alpha + 1/\beta and (\alpha+1)(\beta+1) but I can't think of any rules I know to help me solve the problem.

The Attempt at a Solution



Expanding (\alpha - \beta)2

gives

\alpha2+\beta2 -2\alpha\beta

But I don't know what I can do with this info.

I'd appreciate a nudge in the right direction!

Thanks

##(\alpha - \beta)^2 = (\alpha + \beta)^2 - 4\alpha\beta##
You said that you have already calculated ##\alpha + \beta ## and ##\alpha\beta ##.
 
Mark44 said:
##(\alpha - \beta)^2 = (\alpha + \beta)^2 - 4\alpha\beta##
You said that you have already calculated ##\alpha + \beta ## and ##\alpha\beta ##.

Gah, I should have seen that.

Thanks!
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Similar threads

To prove that a given quadratic has integral roots
Replies
20
Views
2K
Both roots of a quadratic equation above and below a number
Replies
7
Views
2K
Find the value of alpha and beta (matrix equation)
Replies
15
Views
4K
Finding an angle of a triangle as function of another angle
Replies
21
Views
3K
Solving equations of the form ##a\sin\theta+b\cos\theta = c##
Replies
2
Views
2K
Rope between inclines with maximum length of hanging middle portion
Replies
46
Views
2K
I Solving a system of equations with 5 unknowns
Replies
10
Views
938
A proof in the Hilbert-style axiom system
Replies
2
Views
2K
Solving 3D Vector Equation for ##\vec{y}##
Replies
16
Views
2K
A Calculate velocity of streams impinging at differing angles
Replies
30
Views
1K

Hot Threads

Recent Insights

Back
Top