Quant Exam > Quant Questions > |x2 - 2x|< xa)l < x < 3 b)—...
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|x2 - 2x| < x
- a)l < x < 3
- b)—1 < x < 3
- c)0 < x < 4
- d)x > 3
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
|x2 - 2x|< xa)l < x < 3 b)—1 < x< 3c)0 <...
Method to Solve :
You can factor x^2+2x=0 as:
x(x+2)=0
Now, we can solve each term for 0:
x=0 - no other work needed,
and
x+2=0
x+2−2=0−2
x+0=−2
x=−2
x(x+2)=0
Now, we can solve each term for 0:
x=0 - no other work needed,
and
x+2=0
x+2−2=0−2
x+0=−2
x=−2
Most Upvoted Answer
|x2 - 2x|< xa)l < x < 3 b)—1 < x< 3c)0 <...
The expression |x2 - 2x| represents the absolute value of the quadratic expression x^2 - 2x.
To find the absolute value of x^2 - 2x, we need to consider the cases when the expression inside the absolute value is positive and negative.
When x^2 - 2x is positive (greater than or equal to zero):
x^2 - 2x ≥ 0
x(x - 2) ≥ 0
In this case, the absolute value of x^2 - 2x is simply x^2 - 2x.
When x^2 - 2x is negative (less than zero):
x^2 - 2x < />
x(x - 2) < />
In this case, the absolute value of x^2 - 2x is -(x^2 - 2x), which is equal to -x^2 + 2x.
Therefore, the expression |x^2 - 2x| can be written as:
x^2 - 2x, for x ≤ 0 or x ≥ 2
-x^2 + 2x, for 0 < x="" />< 2="" />
To find the absolute value of x^2 - 2x, we need to consider the cases when the expression inside the absolute value is positive and negative.
When x^2 - 2x is positive (greater than or equal to zero):
x^2 - 2x ≥ 0
x(x - 2) ≥ 0
In this case, the absolute value of x^2 - 2x is simply x^2 - 2x.
When x^2 - 2x is negative (less than zero):
x^2 - 2x < />
x(x - 2) < />
In this case, the absolute value of x^2 - 2x is -(x^2 - 2x), which is equal to -x^2 + 2x.
Therefore, the expression |x^2 - 2x| can be written as:
x^2 - 2x, for x ≤ 0 or x ≥ 2
-x^2 + 2x, for 0 < x="" />< 2="" />
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|x2 - 2x|< xa)l < x < 3 b)—1 < x< 3c)0 < x < 4 d)x > 3Correct answer is option 'A'. Can you explain this answer?
Question Description
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