Quadratic discriminant with tricky algebra

[sooyong94]

Homework Statement

Homework Equations

Quadratic discriminant

The Attempt at a Solution

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

 

[Ray Vickson]

Homework Statement

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.

 

[sooyong94]

I got something like
ab-4ac-ad+bc+bd-cd but I can't seem to work around that.

 

[Irene Kaminkowa]

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.

 

[Ray Vickson]

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.

 

[sooyong94]

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.

 

[sooyong94]

Strangely enough I got -b^2 -4ac, which isn't right.

Update - I found an algebraic slip in my working.

 

[sooyong94]

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.