discriminants

Iris Aliaj · Poincare Conjecture Offline Joined: 02 Jun 2004 Posts: 165

What are the discriminants?They were mentioned(well,actually they were the weapon for solving the problem) in the solution 3 of the problem 4,round 14,International Mathematical talent search,but i cant write it here cuz i don't know the LaTex.

**Posted:** Wed Jun 16, 2004 2:12 pm

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Lagrangia

If I am not mistaking the the discriminant is $\vartriangle=b^{2}-4ac$ for a second degree ecuation... $ax^{2}+bx+c=0$ . But maybe I didn't understand the question.. Blush

**Posted:** Thu Jun 17, 2004 2:31 am

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Iris Aliaj · Poincare Conjecture Offline Joined: 02 Jun 2004 Posts: 165

You're not mistaken Smile

.By looking at the solution in view of your reply,i realised you were right,but there's sth i don't understand.In the solution of my problem it's stated:

"a(ax + y) + 1 = a2x + ay + 1 must be a perfect square, hence its discriminant, y2 � 4x, should vanish"

Why should the disriminant vanish?? maybe

**Posted:** Thu Jun 17, 2004 7:12 am

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dante · P versus NP Offline Joined: 12 Jun 2004 Posts: 28

Because you would be left with a root of a non-square, making the whole thing be irrational.

**Posted:** Thu Jun 17, 2004 3:46 pm

Iris Aliaj · Poincare Conjecture Offline Joined: 02 Jun 2004 Posts: 165

Why y ² -4x is a non square?if it's a square(a perfect one)then it's not necessarey to have the discriminant vanished.

**Posted:** Thu Jun 17, 2004 10:59 pm

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dante · P versus NP Offline Joined: 12 Jun 2004 Posts: 28

There should be something else in the problem. Could you post the solution or at least the problem so that we can know exactly what x,y are and what parameters they meet?

**Posted:** Tue Jun 22, 2004 5:32 pm

DiaDi

it's about de whole ecuation being a perfect square.....not about the discriminant!that's why the discriminant should be 0!

**Posted:** Wed Oct 20, 2004 7:44 am

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Leonardo

What they meant is that if you want any cuadratic
$ax^2+bx+c=0$
To be a perfect square, both roots must be equal, or what is the same, the discriminant $b^2-4ac$ must vanish.

**Posted:** Tue Feb 22, 2005 4:21 pm

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bomb · Riemann Hypothesis Offline Joined: 29 Sep 2004 Posts: 363

To first guy, discriminant of a polynomial is defined by products of its roots, it is used to determine realness of the roots of a polynomail.

Bomb

**Posted:** Wed Sep 07, 2005 10:46 pm

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enescu

See http://mathworld.wolfram.com/PolynomialDiscriminant.html

**Posted:** Sat Sep 10, 2005 7:54 am

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