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How many real solutions exist for the equation x2 – 11|x| - 60 = 0?
- a)3
- b)2
- c)1
- d)4
- e)None
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
How many real solutions exist for the equation x2– 11|x| - 60 = ...
Step 1: Assign y = |x| and solve for y
Let |x| = y.
We can rewrite the equation x2 - 11|x| - 60 = 0 as y2 - 11y - 60 = 0
The equation can be factorized as y2 - 15y + 4y - 60 = 0
(y - 15) (y + 4) = 0
The values of y that satisfy the equation are y = 15 or y = -4.
We can rewrite the equation x2 - 11|x| - 60 = 0 as y2 - 11y - 60 = 0
The equation can be factorized as y2 - 15y + 4y - 60 = 0
(y - 15) (y + 4) = 0
The values of y that satisfy the equation are y = 15 or y = -4.
Step 2: Compute number of real values of x
We have assigned y = |x|
|x| is always a non-negative number.
So, |x| cannot be -4.
|x| can take only one value = 15.
If |x| = 15, x = 15 or -15.
|x| is always a non-negative number.
So, |x| cannot be -4.
|x| can take only one value = 15.
If |x| = 15, x = 15 or -15.
The number of real solutions that exist for x2 – 11|x| - 60 = 0 is 2.
The correct choice is (B) and the correct answer is 2.
Most Upvoted Answer
How many real solutions exist for the equation x2– 11|x| - 60 = ...
Analysis:
To find the number of real solutions for the given equation x^2 - 11|x| - 60 = 0, we need to consider two cases: when x is positive and when x is negative.
Case 1: x is positive
When x is positive, the equation becomes x^2 - 11x - 60 = 0.
Factoring the equation, we get (x - 15)(x + 4) = 0.
This gives us two possible solutions: x = 15 and x = -4.
Case 2: x is negative
When x is negative, the equation becomes x^2 + 11x - 60 = 0.
Factoring the equation, we get (x + 15)(x - 4) = 0.
This gives us two possible solutions: x = -15 and x = 4.
Combining the solutions:
Since we are looking for real solutions, we can see that only x = 4 is a valid solution that satisfies the absolute value requirement. Therefore, there are 2 real solutions for the equation x^2 - 11|x| - 60 = 0.
Therefore, the correct answer is option B) 2.
To find the number of real solutions for the given equation x^2 - 11|x| - 60 = 0, we need to consider two cases: when x is positive and when x is negative.
Case 1: x is positive
When x is positive, the equation becomes x^2 - 11x - 60 = 0.
Factoring the equation, we get (x - 15)(x + 4) = 0.
This gives us two possible solutions: x = 15 and x = -4.
Case 2: x is negative
When x is negative, the equation becomes x^2 + 11x - 60 = 0.
Factoring the equation, we get (x + 15)(x - 4) = 0.
This gives us two possible solutions: x = -15 and x = 4.
Combining the solutions:
Since we are looking for real solutions, we can see that only x = 4 is a valid solution that satisfies the absolute value requirement. Therefore, there are 2 real solutions for the equation x^2 - 11|x| - 60 = 0.
Therefore, the correct answer is option B) 2.
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How many real solutions exist for the equation x2– 11|x| - 60 = 0?a)3b)2c)1d)4e)NoneCorrect answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about How many real solutions exist for the equation x2– 11|x| - 60 = 0?a)3b)2c)1d)4e)NoneCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many real solutions exist for the equation x2– 11|x| - 60 = 0?a)3b)2c)1d)4e)NoneCorrect answer is option 'B'. Can you explain this answer?.
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