
Determinant
is given with m and n real numbers and it's solutions.
It's asked for the value of the determinant:
I have tried to solve it in the Vandermonde way
Or to sum up columns 2 and 3 to the first (to obtain the sum, and the sum of squares of the solutions  which are found easily with Viete).
I have managed to find out that:
the value of the determinant beeing thinking that I should sqare the first identety and make some conection with this one.
I'm sorry for posting this problem to prealgebra too. This is a linear algebra problem, but it's for highschool.

Let the roots of be , and . Then , and .
Here's one way to find , probably not the best.
Start with , and so .
Since is a root, , so . So now .
Therefore . Similarly and .
Thus .
Using the root relations, this last quantity is . Hope this helps.

It was very helpful. I have found out, in other place, antoher method.
Thank you very much, this one I have understood it.

I will post the other solution, it's not so complicated.
Let it be
hope transposed is the name in English.
From Viete's relations:
I didn't solve it. Someone from another forum (from my country) did. Hope it helps others too.