GMAT Club Olympics 2024 (Day 1): If 2 is one solution of the equation

Question

If 2 is one solution of the equation  x^2 + b^2x = 12 , where b is a constant, which of the following could be the value of  bx ?

I. -12
II. 8
III. 12

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

Bunuel · Accepted Answer

GMAT Club Official Explanation:

Substituting x = 2 into the equation, we get:

4 + 2b^2 = 12

b^2 = 4

Hence, the equation is  x^2 + 4x = 12 , which simplifies to  (x - 2)(x + 6) = 0 , and thus  x = 2  or  x = -6 .

Note that the question asks for the value of  bx , not  b^2x . Since  b^2 = 4  gives us b = -2 or b = 2, the possible values for  bx  could be (-2)*2 = -4, 2*2 = 4, (-2)*(-6) = 12, and (-2)*6 = -12.

Answer: E.

jairovx · Answer

Given:
 
 One solution is 2, so x = 2. 
 Replace x = 2 in the equation 2^2+(b^2)x=12, solve for b = +2, -2. 
 Solve the equation with the new value of b, check that it doesn't matter +,- because it is square, so x^2+4*x=12, then the solutions x = 2, x = -6  
 For x=2

b= 2, then bx = 4 
 b= -2, then bx = -4  
 For x=−6

b= 2, then bx = -12 
 b= -2, then bx = +12  
So, the possible values of bx are 4,−4,12−12.

Given the options:

I. -12 
 II. 8 
 III. 12  
The correct answer choices that match our results are:

I. -12 
 III. 12  
Thus, the correct answer is:

E. I and III only

muddassirmoolji · Answer

x^2 + b^2x = 12

Now, One of the Solutions is 2. This Means we need to break down this equation into (x-2)(x-a)
Such That (x-2)(x-a)= x^2 + b^2x - 12

Solving through Assumption,

x^2 - 2x + 6x -12 = 0
x (x-2) +6 (x-2) = 0

(x-2)(x+6) = 0

Now Equating This With (x-2)(x-a), we get a = -6

x^2 - 2x + 6x -12 = 0 can be re written as x^2 +4x = 12

Hence, B^2 = 4.... b = -2 or 2

And X= - 6 or 2

Possible Values of Bx are 12(-2 * -6), -12 (2*-6) , 4 (2*2) & -4(2*-2)

1616 · Answer

x^2 + b^2x - 12  = 0

In an equation like ax^2 + bx + c = 0
Sum of the roots = -b/a
Product of roots = c/a

Now in our case, let the two roots be m and n,

m + n = -b^2/1
m*n = -12/1

now one of the root is 2, so let say m = 2
So n = -6
m+n = -4 = -b^2
b = +2 or -2

Case I bx = -12,
So either x = 6 if b = -2  --> then putting the value in equation --> 36 + 24 - 12 = 48 and is not equal to zero, hence not possible
 or x = -6 if b = 2 --> then putting the value in the equation --> 36 - 24 - 12 = 0, hence could be the solution.

Case II bx = 8, so b = 2, x = 4 --> then putting the value in equation --> 16 + 16 - 12 = 20 and is not equal to zero, hence not possible
or b = -4, x = -2 --> then putting the value in equation --> 4 - 32 - 12 = -40 and is not equal to zero, hence not possible

Case III
So either x = 6 if b = 2  --> then putting the value in equation --> 36 + 24 - 12 = 48 and is not equal to zero, hence not possible
 or x = -6 if b = -2 --> then putting the value in the equation --> 36  - 24 - 12 = 0, hence could be the solution.

So answer is I and III

ablatt4 · Answer

Plug 2 in for X

4+2b^2 = 12
2b^2 = 8
b^2= 4
b= 2, -2

plug 2 or -2 back in and solve the other x

x=2,-6

b=2,-2

2*-6=-12

-2*-6 = 12

nothing here makes 8 so E is correct

GMAT Club Olympics 2024 (Day 1): If 2 is one solution of the equation

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

GMAT Club Olympics 2024 (Day 1): ­If 2 is one solution of the equation

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Club Olympics 2024 (Day 1): If 2 is one solution of the equation