Quadratic equation

[shashank.ism]

A quadratic with integral coefficients has two distinct positive integers as roots, the sum of its coefficients is prime and it takes the value -55 for some integer. The sum of the roots is

A) 32
B) 20
C) 24
D) 36
E) None of these

[spoiler]Correct Answer: B[/spoiler]

Problem approach needed..

[money9111]

i dont understand the question... mainly "it takes the value -55 for some integer."

[papgust]

I pretty much doubt whether we will be tested with these concepts in GMAT.

[money9111]

surely hope not, but I think I just didn't understand the question... is this question from a GMAT book?

[Brent@GMATPrepNow]

i dont understand the question... mainly "it takes the value -55 for some integer."

The question tells us that we have an equation in the form ax^2 + bx + c = 0
a, b and c are integers.
There are two different solutions to the equation, and these solutions are positive integers.
The sum a+b+c is a prime number.
There is some integer k such that ak^2 + bk + c = -55

Having said all of that, this question is totally out of scope, so you can focus your energies elsewhere.

[vscid]

I think we really need to put that project of rating questions on fast track !!

[harsh.champ]

i dont understand the question... mainly "it takes the value -55 for some integer."

The question tells us that we have an equation in the form ax^2 + bx + c = 0
a, b and c are integers.
There are two different solutions to the equation, and these solutions are positive integers.
The sum a+b+c is a prime number.
There is some integer k such that ak^2 + bk + c = -55

Having said all of that, this question is totally out of scope, so you can focus your energies elsewhere.

Well Brent,
I think this is a challenge question which is only useful for brainstorming and for fun.It hopefully would not come on the GMAT.

As for money9111:-

i dont understand the question... mainly "it takes the value -55 for some integer."

It just means that the sum of the coefficients is a prime and it(it here means the quadratic eqn.) takes the value -55 when we take some integer x.
Now,a+b+c=prime no.
ax2 + bx + c =-55
In my case I would solve the question my plugging prime numbers.


On another note Brent,Is there any formal approach for solving the ques.[(Ex:-Elimination technique and by the use of SUM(-b/a) and PRODUCT(c/a) and the fact that both of them are integers]

[ajith]

In my case I would solve the question my plugging prime numbers.

Please illustrate, which you would not!

[harsh.champ]

In my case I would solve the question my plugging prime numbers.

Please illustrate, which you would not!

Well,why would I not....[I had not written in detail since I was not very sure abt the approach.I tried to look for some properties on the net and found a Dirichlet Theorem that deals with ques. involving prime coefficients.I got confused and tried to solve it in my own way]
Anyways it goes like this:-the roots are two distinct +ve integers .
So,their sum and pdt both will be +ve.
Which means either c and a are both -ve.[b is +ve then]
or b is -ve [a and c are then positive]
Now, lets take the 1st prime no. 2.
a = 2 b= -1 c=+1
Now,I will look for x when the quadratic becomes -55.
Then,the next no...............So,this way the hit-and-trial goes on..


I found this a very long method and thus asked Brent if he has any formal method.