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

Question

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

Bunuel · Accepted Answer

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.

ENGRTOMBA2018 · Answer

Do not post multiple posts for the same doubt. Give the experts/posters some time to reply to your earlier post.

As for your question, refer to the text below:

For a quadratic equation  ax^2+bx+c=0 , with a 
eq 0

Discriminant,  D = b^2-4ac

For a quadratic equation to have  2  distinct  real roots :  D > 0

For a quadratic equation to have  2  equal  real roots :  D = 0

For a quadratic equation to have  0 distinct real roots :  D < 0

Coming back to the quadratic equation,  x^2-7x+q=0  ---> for equal roots,  D =0  --->  (-7)^2-4*q*1 = 0  --->  49=4q --->  q= 49/4 = 12.25

Hope this helps.

Eshika · Answer

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

Bunuel · Answer

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.

Eshika · Answer

Yeah I gt that..My mistake...

anilnandyala · Answer

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

Eshika · Answer

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.

anik19890 · Answer

can you please explain this  As it has equal roots then its discriminant must equal to zero  i can not understand

law258 · Answer

Use quadratic formula.

--> 7 +-  /2

Try values in for C. The correct one should give you the same two values once the equation is solved

Alex75PAris · Answer

x²+px+12=0

if 4 is a root, then

(x - 4) ( x +r2) = 0 ; R2 being the other root.
So, -4*r2 = 12 => r2 = -7

So, x²+px+q= x²-7x+q=0

We know that this equation has only one root, thus :
(x+r)²=0=x²+2xr+r²=0

So, q=r² and 2r=-7
r=-7/2, and q=r²=49/4

Answer choice A

Manonamission · Answer

x^2+px+12=0 is 4

One root is given as 4 => Substituting the values

4p +28 = 0

p = -7

Second eqn x^2+px+q=0

x^2 -7x + q = 0

q = 49/4 A

deeeuce · Answer

Hi Experts,
does equal root mean just one root?

Thanks

bumpbot · Answer

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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

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