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Quadratic equation

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Quadratic equation

by shashank.ism » Thu Feb 11, 2010 7:50 am
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..
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by money9111 » Thu Feb 11, 2010 8:21 am
i dont understand the question... mainly "it takes the value -55 for some integer."
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by papgust » Thu Feb 11, 2010 8:25 am
I pretty much doubt whether we will be tested with these concepts in GMAT.
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by money9111 » Fri Feb 12, 2010 6:35 pm
surely hope not, but I think I just didn't understand the question... is this question from a GMAT book?
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by Brent@GMATPrepNow » Sat Feb 13, 2010 9:26 am
money9111 wrote: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.
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by vscid » Sat Feb 13, 2010 1:03 pm
I think we really need to put that project of rating questions on fast track !!
The GMAT is indeed adaptable. Whenever I answer RC, it proficiently 'adapts' itself to mark my 'right' answer 'wrong'.
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by harsh.champ » Thu Feb 18, 2010 6:21 am
Brent Hanneson wrote:
money9111 wrote: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]
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by ajith » Thu Feb 18, 2010 6:27 am
harsh.champ wrote:
In my case I would solve the question my plugging prime numbers.
Please illustrate, which you would not!
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by harsh.champ » Thu Feb 18, 2010 6:50 am
ajith wrote:
harsh.champ wrote:
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.
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



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