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In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A): The equation x2 + 2ax - b2 = 0 can have repeated roots, where a,b are real numbers.
Reason(R): The equation Ax2 + Bx + C = 0 will have repeated roots when the determinant becomes zero.
Assertion(A): The equation x2 + 2ax - b2 = 0 can have repeated roots, where a,b are real numbers.
Reason(R): The equation Ax2 + Bx + C = 0 will have repeated roots when the determinant becomes zero.
- a)Both Assertion and Reason are true and Reason is the correct explanation of assertion.
- b)Both Assertion and Reason are true and Reason is not the correct explanation of assertion.
- c)Assertion is true but Reason is false.
- d)Assertion is false but Reason is true.
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
In the following question, a Statement of Assertion (A) is given follo...
Statement:
Assertion (A): The equation x^2 - 2ax - b^2 = 0 can have repeated roots, where a,b are real numbers.
Reason (R): The equation Ax^2 - Bx - C = 0 will have repeated roots when the determinant becomes zero.
Explanation:
To understand why the correct answer is option 'D', let's analyze each statement separately.
Statement A: The equation x^2 - 2ax - b^2 = 0 can have repeated roots, where a,b are real numbers.
A quadratic equation can have two roots, and these roots can be real or complex numbers. When a quadratic equation has repeated roots, it means both roots are the same. In other words, the quadratic equation has only one distinct root.
For the given equation x^2 - 2ax - b^2 = 0 to have repeated roots, the discriminant of the equation should be equal to zero.
Statement R: The equation Ax^2 - Bx - C = 0 will have repeated roots when the determinant becomes zero.
The determinant of the quadratic equation Ax^2 - Bx - C = 0 is given by the expression B^2 - 4AC. If the determinant is equal to zero, then the quadratic equation will have repeated roots.
Now, let's compare the given statements:
The equation x^2 - 2ax - b^2 = 0 can have repeated roots if and only if the discriminant, which is (-2a)^2 - 4(1)(-b^2), is equal to zero. Simplifying this expression, we get:
4a^2 + 4b^2 = 0
Dividing both sides by 4, we have:
a^2 + b^2 = 0
Since both a^2 and b^2 are non-negative (as they are squares of real numbers), the only way for their sum to be zero is if both a and b are equal to zero.
Therefore, the given equation x^2 - 2ax - b^2 = 0 can have repeated roots only when a = 0 and b = 0.
However, the reason given in Statement R is a general statement applicable to any quadratic equation. It does not specifically address the conditions required for the given equation x^2 - 2ax - b^2 = 0 to have repeated roots.
Hence, the correct answer is option 'D' - Assertion is false but Reason is true.
Assertion (A): The equation x^2 - 2ax - b^2 = 0 can have repeated roots, where a,b are real numbers.
Reason (R): The equation Ax^2 - Bx - C = 0 will have repeated roots when the determinant becomes zero.
Explanation:
To understand why the correct answer is option 'D', let's analyze each statement separately.
Statement A: The equation x^2 - 2ax - b^2 = 0 can have repeated roots, where a,b are real numbers.
A quadratic equation can have two roots, and these roots can be real or complex numbers. When a quadratic equation has repeated roots, it means both roots are the same. In other words, the quadratic equation has only one distinct root.
For the given equation x^2 - 2ax - b^2 = 0 to have repeated roots, the discriminant of the equation should be equal to zero.
Statement R: The equation Ax^2 - Bx - C = 0 will have repeated roots when the determinant becomes zero.
The determinant of the quadratic equation Ax^2 - Bx - C = 0 is given by the expression B^2 - 4AC. If the determinant is equal to zero, then the quadratic equation will have repeated roots.
Now, let's compare the given statements:
The equation x^2 - 2ax - b^2 = 0 can have repeated roots if and only if the discriminant, which is (-2a)^2 - 4(1)(-b^2), is equal to zero. Simplifying this expression, we get:
4a^2 + 4b^2 = 0
Dividing both sides by 4, we have:
a^2 + b^2 = 0
Since both a^2 and b^2 are non-negative (as they are squares of real numbers), the only way for their sum to be zero is if both a and b are equal to zero.
Therefore, the given equation x^2 - 2ax - b^2 = 0 can have repeated roots only when a = 0 and b = 0.
However, the reason given in Statement R is a general statement applicable to any quadratic equation. It does not specifically address the conditions required for the given equation x^2 - 2ax - b^2 = 0 to have repeated roots.
Hence, the correct answer is option 'D' - Assertion is false but Reason is true.
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In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A): The equation x2 + 2ax - b2 = 0 can have repeated roots, where a,b are real numbers.Reason(R): The equation Ax2 + Bx + C = 0 will have repeated roots when the determinant becomes zero.a)Both Assertion and Reason are true and Reason is the correct explanation of assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'D'. Can you explain this answer?
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In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A): The equation x2 + 2ax - b2 = 0 can have repeated roots, where a,b are real numbers.Reason(R): The equation Ax2 + Bx + C = 0 will have repeated roots when the determinant becomes zero.a)Both Assertion and Reason are true and Reason is the correct explanation of assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A): The equation x2 + 2ax - b2 = 0 can have repeated roots, where a,b are real numbers.Reason(R): The equation Ax2 + Bx + C = 0 will have repeated roots when the determinant becomes zero.a)Both Assertion and Reason are true and Reason is the correct explanation of assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A): The equation x2 + 2ax - b2 = 0 can have repeated roots, where a,b are real numbers.Reason(R): The equation Ax2 + Bx + C = 0 will have repeated roots when the determinant becomes zero.a)Both Assertion and Reason are true and Reason is the correct explanation of assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'D'. Can you explain this answer?.
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A): The equation x2 + 2ax - b2 = 0 can have repeated roots, where a,b are real numbers.Reason(R): The equation Ax2 + Bx + C = 0 will have repeated roots when the determinant becomes zero.a)Both Assertion and Reason are true and Reason is the correct explanation of assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A): The equation x2 + 2ax - b2 = 0 can have repeated roots, where a,b are real numbers.Reason(R): The equation Ax2 + Bx + C = 0 will have repeated roots when the determinant becomes zero.a)Both Assertion and Reason are true and Reason is the correct explanation of assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A): The equation x2 + 2ax - b2 = 0 can have repeated roots, where a,b are real numbers.Reason(R): The equation Ax2 + Bx + C = 0 will have repeated roots when the determinant becomes zero.a)Both Assertion and Reason are true and Reason is the correct explanation of assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'D'. Can you explain this answer?.
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