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Roots of eqn

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by harsh.champ » Wed Feb 17, 2010 6:20 am
If a+b+c=0, then the quadratic eqn "3a(x ^2 )+ 2bx + c = 0 " has



(A)real and different roots
(B)imaginary roots
(C)rational roots
(D)real and equal roots
(E)None of the above
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by money9111 » Wed Feb 17, 2010 8:20 am
is this even a GMAT problem? I have never encountered anything pertaining to real/imaginary numbers in any of my prep... maybe i just haven't gotten that far yet
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by shashank.ism » Wed Feb 17, 2010 8:48 am
I think this type of problem never gonna bump in GMAT real test. Its a real tough question. If in any case it flashes on screen its hard luck...
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by money9111 » Wed Feb 17, 2010 9:02 am
huh?
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by ajith » Wed Feb 17, 2010 9:04 am
money9111 wrote:is this even a GMAT problem? I have never encountered anything pertaining to real/imaginary numbers in any of my prep... maybe i just haven't gotten that far yet
I do not think this is anyway near a Real GMAT problem, I choose to ignore it in my preps
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by money9111 » Wed Feb 17, 2010 9:06 am
good idea...

question - harsh.champ when you post questions that aren't GMATquestions can you let us know upfront? I think that might clarify things a bit more... thanks
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by harsh.champ » Thu Feb 18, 2010 12:06 am
money9111 wrote:good idea...

question - harsh.champ when you post questions that aren't GMATquestions can you let us know upfront? I think that might clarify things a bit more... thanks
Hey money9111,
You are right that this is not one of the GMAT questions.I had just posted this as a challenge question that requires brainstorming.Form the next time,I will surely write "Challenge Question" in bracket.I guess then people will see the question in a different light.Thanks!!


All said and done,can anybody come up with the soln. approach?[Calling the math whizsss over here:)]
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by mohit11 » Thu Feb 18, 2010 12:24 am
Not that difficult.

a + b + c = 0 ....1

and equation is 3a(x ^2 )+ 2bx + c = 0 ....2

Lets assume A = 1 , B = 2 , C = -3 , hence equation one is satisfied.

Put in these values in equation 2

3(x ^2 )+ 4x - 3 = 0

Roots of the equation aX^2 + bx + c =0 are - b +/- squar root (b^2 - 4ac)/2a

Which gives... -4 +/- sq root (-20)/ 6 or -4 +/- sq root 20i /6

Hence answer is... Imaginary Roots B
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