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Quadratic discriminant with tricky algebra

  • #1
173
2

Homework Statement


Capture.png


Homework Equations


Quadratic discriminant

The Attempt at a Solution


I did b^2 -4ac>=0, but the algebra becomes prohibitively difficult.
 

Answers and Replies

  • #2
Ray Vickson
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Homework Statement


Capture.png


Homework Equations


Quadratic discriminant

The Attempt at a Solution


I did b^2 -4ac>=0, but the algebra becomes prohibitively difficult.
Sometimes there are just no shortcuts, and lengthy algebra cannot be avoided. That being said, I am not sure the result sought is correct; in particular, in your second equation you have a constant ##d## appearing in it, but there is no ##d## in the first equation.
 
  • #3
173
2
I got something like
ab-4ac-ad+bc+bd-cd but I can't seem to work around that.
 
  • #4
In the second equation there is a misprint
The correct equation is
(a+c-b)x2-2(a-c)x+(a+c+b) = 0
The proof is not difficult. Just find the discriminant.
 
  • #5
Ray Vickson
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I got something like
ab-4ac-ad+bc+bd-cd but I can't seem to work around that.
What about the issue I raised? There is a ##d## in the second equation, but no ##d## in the first one. The relation between ##a,b,c## arising from the first equation does not involve any ##d## at all.
 
  • #6
173
2
In the second equation there is a misprint
The correct equation is
(a+c-b)x2-2(a-c)x+(a+c+b) = 0
The proof is not difficult. Just find the discriminant.
Thanks - I guess there's a misprint in my book after all.
 
  • #7
173
2
Strangely enough I got -b^2 -4ac, which isn't right.

Update - I found an algebraic slip in my working.
 
  • #8
173
2
I have managed to work the first part - but I don't have a clue on tackle the second part.

Update - I managed to work this out.
 
Last edited:

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