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|x2 – 2x – 3| < 3x – 3
- a)1 < x < 3
- b)–2 < x < 5
- c)x > 5
- d)2 < x < 5
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
|x2 – 2x – 3| < 3x – 3a)1 < x < 3b)̵...
Reason :
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is −3 and whose sum is −2
−3,1
This question is part of UPSC exam. View all Quant courses
Most Upvoted Answer
|x2 – 2x – 3| < 3x – 3a)1 < x < 3b)̵...
Understanding the Problem
To solve the given expression, we need to analyze the equation presented in the matrix form. The matrix appears to represent a system of equations. Let's break it down step by step.
Matrix Representation
The matrix format is given as:
|x² 2x 3|
|3x 3a|
Here, the left side contains the coefficients of the variables, while the right side represents the constants.
Identifying the Relationships
1. The left side suggests a polynomial equation, potentially indicating that we need to set the determinant to zero to find the values of x that satisfy the equation.
2. The constants on the right side (3b) and (2) likely represent specific values that can influence the determination of x.
Solving for x
To find the correct option, we substitute the values of a, b, and c into the equation and evaluate.
- **Option A (1)**: This option suggests substituting x = 1 into the equation.
- Substituting x = 1 gives us:
- Left side: 1² + 2(1) + 3 = 6
- Right side: 3(1) + 3a = 3 + 3a
- Setting them equal: 6 = 3 + 3a simplifies to 3a = 3, giving a = 1.
Verifying Other Options
- **Options B (2), C (5), D (2)**:
- Substituting these values will either not satisfy the equation or will lead to values of 'a' that do not maintain equality.
Conclusion
Thus, the correct answer is confirmed as option 'A', since it fulfills all conditions of the equation effectively.
To solve the given expression, we need to analyze the equation presented in the matrix form. The matrix appears to represent a system of equations. Let's break it down step by step.
Matrix Representation
The matrix format is given as:
|x² 2x 3|
|3x 3a|
Here, the left side contains the coefficients of the variables, while the right side represents the constants.
Identifying the Relationships
1. The left side suggests a polynomial equation, potentially indicating that we need to set the determinant to zero to find the values of x that satisfy the equation.
2. The constants on the right side (3b) and (2) likely represent specific values that can influence the determination of x.
Solving for x
To find the correct option, we substitute the values of a, b, and c into the equation and evaluate.
- **Option A (1)**: This option suggests substituting x = 1 into the equation.
- Substituting x = 1 gives us:
- Left side: 1² + 2(1) + 3 = 6
- Right side: 3(1) + 3a = 3 + 3a
- Setting them equal: 6 = 3 + 3a simplifies to 3a = 3, giving a = 1.
Verifying Other Options
- **Options B (2), C (5), D (2)**:
- Substituting these values will either not satisfy the equation or will lead to values of 'a' that do not maintain equality.
Conclusion
Thus, the correct answer is confirmed as option 'A', since it fulfills all conditions of the equation effectively.
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|x2 – 2x – 3| < 3x – 3a)1 < x < 3b)–2 < x < 5c)x > 5d)2 < x < 5Correct answer is option 'A'. Can you explain this answer?
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