How many values of x satisfy

Question

How many values of  x  satisfy the equation  x^{3} = 16x ?

(A) 0  
(B) 1  
(C) 2  
(D) 3  
(E) 4

GMATNinja · Answer

Check out question 3 in the video below for the solution:

https://www.youtube.com/watch?v=6Kyt7nWkkqk&t=1577s

Jsgambach · Answer

Rewrite as: x^3 - 16x = 0
Then factor out x and obtain x (x^2 - 16) = 0

(x^2 - 16) is (x+4)(x-4)

At this point we get x (x-4) (x+4) = 0
Hence x could equal -4 , 0 or 4. 3 possible values.

Answer Choice D

Abhishek009 · Answer

x^3 - 16x = 0

Or,  x(x^2 - 16) = 0

Or,  x(x + 4)(x - 4) = 0 
 
So, Clearly 3 possible values are possible,  x = 0 ,  x = +4  &  x = -4 , Answer must be (C) 3

Demonicgod · Answer

Step 1. Bring all terms to one side:
x3−16x=0x^3 - 16x = 0x3−16x=0
 
Step 2. Factor out xxx:
x(x2−16)=0x(x^2 - 16) = 0x(x2−16)=0
 
Step 3. Factor the quadratic:
x(x−4)(x+4)=0x(x - 4)(x + 4) = 0x(x−4)(x+4)=0
 
Step 4. Solve for xxx:
Set each factor to zero:
 
 x=0x = 0x=0 
 x−4=0⇒x=4x - 4 = 0 \Rightarrow x = 4x−4=0⇒x=4 
 x+4=0⇒x=−4x + 4 = 0 \Rightarrow x = -4x+4=0⇒x=−4  
 
✅  Total distinct solutions:  3 values
x=−4,0,4x = -4, 0, 4x=−4,0,4
 
✅  Answer: (D) 3

How many values of x satisfy

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GMAT Problem Solving (PS) Questions

How many values of x satisfy

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