A problem related to quadratic equation

[safwane]

I have a nonlinear Diophantine equation of the form
[math]g(x,y)t^2+f(x,y)t+d(x,y)=0[/math] such that t is a positive integer variable and g(x,y),f(x,y),d(x,y) are polynomial functions in the positive integers variables x,y.
Then I am asking if one can consider this equation as a quadratic one in t and apply the well known results about quadratic equations.

 

[Deleted member 4993]

I have a nonlinear Diophantine equation of the form
[math]g(x,y)t^2+f(x,y)t+d(x,y)=0[/math] such that t is a positive integer variable and g(x,y),f(x,y),d(x,y) are polynomial functions in the positive integers variables x,y.
Then I am asking if one can consider this equation as a quadratic one in t and apply the well known results about quadratic equations.

You can surely apply quadratic equation - but may not get useful answers.

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem

 

[topsquark]

I have a nonlinear Diophantine equation of the form
[math]g(x,y)t^2+f(x,y)t+d(x,y)=0[/math] such that t is a positive integer variable and g(x,y),f(x,y),d(x,y) are polynomial functions in the positive integers variables x,y.
Then I am asking if one can consider this equation as a quadratic one in t and apply the well known results about quadratic equations.

Of course! Anything in that form can be solved for t.

However I'd start piecemeal. Look at the discriminant and show how to make that an integer and go from there.

-Dan