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If one root of x^2+px+12=0 is 4, and the equation x^2+px+q=0

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If one root of x^2+px+12=0 is 4, and the equation x^2+px+q=0 [#permalink] New post 09 Dec 2010, 06:39
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62% (02:10) correct 37% (01:50) wrong based on 93 sessions
If one root of x^2+px+12=0 is 4, and the equation x^2+px+q=0 has equal roots then the value of q is

A. 49/4
B. 4/49
C. 4
D. 1/4
E. 12
[Reveal] Spoiler: OA
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Re: equation puzzle [#permalink] New post 09 Dec 2010, 07:06
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feruz77 wrote:
If one root of x^2+px+12=0 is 4, and the equation x^2+px+q=0 has equal roots then the value of q is
a) 49/4
b) 4/49
c) 4
d) 1/4
e) 12


As one of the roots of x^2+px+12=0 is x=4 then substituting we'll get: 16+4p+12=0 --> p=-7.

Now, the second equation becomes x^2-7x+q=0. As it has equal roots then its discriminant must equal to zero: d=49-4q=0 --> q=\frac{49}{4}.

Answer: A.
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Re: equation puzzle [#permalink] New post 16 Dec 2010, 07:31
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Hi

I guess the answer is 12.

X^2+px+12=0 with one root as 4

ie 4+b=-p where b is another root
and 4b=12,then b=3

From second equation X^2+px+q=0 ,as roots are equal ,then first root ie 4 and second root ie b=3 are the roots for second equation as well,making 4*3=q ie 12 Ans E
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Re: equation puzzle [#permalink] New post 16 Dec 2010, 07:42
Expert's post
Eshika wrote:
Hi

I guess the answer is 12.

X^2+px+12=0 with one root as 4

ie 4+b=-p where b is another root
and 4b=12,then b=3

From second equation X^2+px+q=0 ,as roots are equal ,then first root ie 4 and second root ie b=3 are the roots for second equation as well,making 4*3=q ie 12 Ans E


It's given that the roots of x^2+px+q=0 are equal (so given that it has double root), not that the roots of this equation equal to the roots of another: x^2+px+12=0. If it were as you say then we would have q=12 right away:
x^2+px+q=0;
x^2+px+12=0.

OA for this question is A.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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Re: equation puzzle [#permalink] New post 16 Dec 2010, 21:22
Bunuel wrote:
Eshika wrote:
Hi

I guess the answer is 12.

X^2+px+12=0 with one root as 4

ie 4+b=-p where b is another root
and 4b=12,then b=3

From second equation X^2+px+q=0 ,as roots are equal ,then first root ie 4 and second root ie b=3 are the roots for second equation as well,making 4*3=q ie 12 Ans E


It's given that the roots of x^2+px+q=0 are equal (so given that it has double root), not that the roots of this equation equal to the roots of another: x^2+px+12=0. If it were as you say then we would have q=12 right away:
x^2+px+q=0;
x^2+px+12=0.

OA for this question is A.



Yeah I gt that..My mistake...
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Re: equation puzzle [#permalink] New post 18 Dec 2010, 07:25
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Eshika wrote:
Hi

I guess the answer is 12.

X^2+px+12=0 with one root as 4

ie 4+b=-p where b is another root
and 4b=12,then b=3

From second equation X^2+px+q=0 ,as roots are equal ,then first root ie 4 and second root ie b=3 are the roots for second equation as well,making 4*3=q ie 12 Ans E


so the 2 roots of equation are 4 & 3
p = - (4+3) =-7
so 2 eq becomes x^2-7x+q
it is given 2 roots of the equation are same
a=b
a+b =7, 2a=7
a=7/2
q = a^2 = 49/4
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Re: equation puzzle [#permalink] New post 19 Dec 2010, 21:07
feruz77 wrote:
If one root of x^2+px+12=0 is 4, and the equation x^2+px+q=0 has equal roots then the value of q is
a) 49/4
b) 4/49
c) 4
d) 1/4
e) 12




Thanks feruz77,I just started using GMAT club and got to know the concept of kudos after getting a mail that I have received 1 kudos.Will start using them now onwards. :)
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Re: If one root of x^2+px+12=0 is 4, and the equation x^2+px+q=0 [#permalink] New post 27 Sep 2013, 07:59
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Re: If one root of x^2+px+12=0 is 4, and the equation x^2+px+q=0   [#permalink] 27 Sep 2013, 07:59
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