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If x3 + 2x2−Ax has only one of its three real and unequal roots between [-1,3). Then the value of A can lie between?
- a)A ∈ (−∞ , −1) U (15, ∞ )
- b)A ∈ (−∞ ,−1] U [15, ∞ )
- c)A ∈ [15, ∞ )
- d)A ∈ [−1, ∞ )
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If x3 + 2x2−Axhas only one of its three real and unequal roots b...
The given equation can be written as (x2 + 2x − A) = 0
=> x = 0 is one such root which lie between 3 and -1.
=> x2 + 2x − A = 0 must not have a single root between 3 and -1 => f(3)*f(-1) > 0
=> (15-A) (-1-A) > 0
=> (A-15)(A+1) > 0
=> A ∈ (−∞ ,−1) U (15, ∞ )
But the given equation x(x2 + 2x−A) = 0 has unequal roots => x2 + 2x−A = 0 must have real and unequal roots => 4 + 4A > 0 => A > -1.
=> A ∈ [15,∞ )
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If x3 + 2x2−Axhas only one of its three real and unequal roots b...
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If x3 + 2x2−Axhas only one of its three real and unequal roots between [-1,3). Then the value of A can lie between?a)A∈(−∞, −1)U(15,∞)b)A∈(−∞,−1]U[15,∞)c)A ∈[15, ∞)d)A ∈[−1, ∞)Correct answer is option 'C'. Can you explain this answer?
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If x3 + 2x2−Axhas only one of its three real and unequal roots between [-1,3). Then the value of A can lie between?a)A∈(−∞, −1)U(15,∞)b)A∈(−∞,−1]U[15,∞)c)A ∈[15, ∞)d)A ∈[−1, ∞)Correct answer is option 'C'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If x3 + 2x2−Axhas only one of its three real and unequal roots between [-1,3). Then the value of A can lie between?a)A∈(−∞, −1)U(15,∞)b)A∈(−∞,−1]U[15,∞)c)A ∈[15, ∞)d)A ∈[−1, ∞)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x3 + 2x2−Axhas only one of its three real and unequal roots between [-1,3). Then the value of A can lie between?a)A∈(−∞, −1)U(15,∞)b)A∈(−∞,−1]U[15,∞)c)A ∈[15, ∞)d)A ∈[−1, ∞)Correct answer is option 'C'. Can you explain this answer?.
If x3 + 2x2−Axhas only one of its three real and unequal roots between [-1,3). Then the value of A can lie between?a)A∈(−∞, −1)U(15,∞)b)A∈(−∞,−1]U[15,∞)c)A ∈[15, ∞)d)A ∈[−1, ∞)Correct answer is option 'C'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If x3 + 2x2−Axhas only one of its three real and unequal roots between [-1,3). Then the value of A can lie between?a)A∈(−∞, −1)U(15,∞)b)A∈(−∞,−1]U[15,∞)c)A ∈[15, ∞)d)A ∈[−1, ∞)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x3 + 2x2−Axhas only one of its three real and unequal roots between [-1,3). Then the value of A can lie between?a)A∈(−∞, −1)U(15,∞)b)A∈(−∞,−1]U[15,∞)c)A ∈[15, ∞)d)A ∈[−1, ∞)Correct answer is option 'C'. Can you explain this answer?.
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