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The product of all real roots of the equation x2 - |x| - 6 = 0 is
- a)-9
- b)6
- c)9
- d)36
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The product of all real roots of the equation x2- |x| - 6 = 0 isa)-9b)...
Equation is x2 - |x| - 6 = 0
Case I: x > 0. then we have
x2 - x - 6 = 0 (lx| = x)
⇒ (x-3)(x+2) = 0
⇒ x = 3 is the solution as x > 0.
(So x = -2 can’t be solution)
Case II: x < 0. then we have
x2 + x - 6 = 0 (|x| = -x)
⇒ (x + 3)(x - 2) = 0
⇒ x = -3 is the solution as x < 0
(So x = 2 can't be solution)
∴ product of roots = 3. - 3 = -9
Case I: x > 0. then we have
x2 - x - 6 = 0 (lx| = x)
⇒ (x-3)(x+2) = 0
⇒ x = 3 is the solution as x > 0.
(So x = -2 can’t be solution)
Case II: x < 0. then we have
x2 + x - 6 = 0 (|x| = -x)
⇒ (x + 3)(x - 2) = 0
⇒ x = -3 is the solution as x < 0
(So x = 2 can't be solution)
∴ product of roots = 3. - 3 = -9
Most Upvoted Answer
The product of all real roots of the equation x2- |x| - 6 = 0 isa)-9b)...
To find the product of all real roots of the equation x^2 - |x| - 6 = 0, we need to first find the roots of the equation and then find their product. Let's solve the equation step by step:
1. Split the equation based on the absolute value function:
x^2 - |x| - 6 = 0
Since the absolute value of x can be either positive or negative, we have two cases to consider:
Case 1: x ≥ 0
In this case, the absolute value of x is equal to x.
x^2 - x - 6 = 0
Case 2: x < />
In this case, the absolute value of x is equal to -x.
x^2 + x - 6 = 0
2. Solve each case separately:
Case 1: x ≥ 0
To solve x^2 - x - 6 = 0, we can factorize the quadratic equation:
(x - 3)(x + 2) = 0
Setting each factor to zero, we get two possible solutions:
x - 3 = 0 -> x = 3
x + 2 = 0 -> x = -2
Case 2: x < />
To solve x^2 + x - 6 = 0, we can again factorize the quadratic equation:
(x - 2)(x + 3) = 0
Setting each factor to zero, we get two more possible solutions:
x - 2 = 0 -> x = 2
x + 3 = 0 -> x = -3
3. Combine the solutions from both cases:
The common solutions to both cases are x = -2 and x = 2.
4. Find the product of the real roots:
The product of all real roots is (-2) * (2) = -4.
Hence, the correct answer is option A) -4.
1. Split the equation based on the absolute value function:
x^2 - |x| - 6 = 0
Since the absolute value of x can be either positive or negative, we have two cases to consider:
Case 1: x ≥ 0
In this case, the absolute value of x is equal to x.
x^2 - x - 6 = 0
Case 2: x < />
In this case, the absolute value of x is equal to -x.
x^2 + x - 6 = 0
2. Solve each case separately:
Case 1: x ≥ 0
To solve x^2 - x - 6 = 0, we can factorize the quadratic equation:
(x - 3)(x + 2) = 0
Setting each factor to zero, we get two possible solutions:
x - 3 = 0 -> x = 3
x + 2 = 0 -> x = -2
Case 2: x < />
To solve x^2 + x - 6 = 0, we can again factorize the quadratic equation:
(x - 2)(x + 3) = 0
Setting each factor to zero, we get two more possible solutions:
x - 2 = 0 -> x = 2
x + 3 = 0 -> x = -3
3. Combine the solutions from both cases:
The common solutions to both cases are x = -2 and x = 2.
4. Find the product of the real roots:
The product of all real roots is (-2) * (2) = -4.
Hence, the correct answer is option A) -4.
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The product of all real roots of the equation x2- |x| - 6 = 0 isa)-9b)6c)9d)36Correct answer is option 'A'. Can you explain this answer? for IIT JAM 2025 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about The product of all real roots of the equation x2- |x| - 6 = 0 isa)-9b)6c)9d)36Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for IIT JAM 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The product of all real roots of the equation x2- |x| - 6 = 0 isa)-9b)6c)9d)36Correct answer is option 'A'. Can you explain this answer?.
The product of all real roots of the equation x2- |x| - 6 = 0 isa)-9b)6c)9d)36Correct answer is option 'A'. Can you explain this answer? for IIT JAM 2025 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about The product of all real roots of the equation x2- |x| - 6 = 0 isa)-9b)6c)9d)36Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for IIT JAM 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The product of all real roots of the equation x2- |x| - 6 = 0 isa)-9b)6c)9d)36Correct answer is option 'A'. Can you explain this answer?.
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