Quadraining Equation #1

Algebra Level 4

$a, b, c$ are distinct real numbers.

If each pair of equations $x^2+ax+b=0$ , $x^2+bx+c=0$ and $x^2+cx+a=0$ has a common root then product of all common roots is :-

2\sqrt{abc}

\sqrt{abc}

2\sqrt{ab+bc+ca}

-1

\sqrt{ab+bc+ca}

\sqrt{2}

1 solution

Parv Maurya
Feb 9, 2015

let the roots of the equations be p ,q,r respectively. then pq=b, qr=c, pq=a so on multiplying them we get pqr is equal to uner root of abc

No, all that you have is $( pqr) ^2 = abc$ . So the conclusion is that $pqr = \pm \sqrt{ abc }$ .

And in fact, we have $pqr = - \sqrt{ abc}$ instead.

Calvin Lin Staff - 6 years, 3 months ago

i also did it the same way but the answer shows -1.

manu dude - 6 years, 1 month ago

https://brilliant.org/problems/find-the-areaonly-your-logic-can-help-you/?group=3UHxOzwinQpA&ref_id=384997

PLEASE TRY TO DO THIS AWSOME PROBLEM TOO..post a solution if you get......................i am waiting for an awesome solution that i made while creating this problem

Yash Sharma - 6 years, 3 months ago

Quadraining Equation #1

1 solution

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