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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : If roots of the equation x2 - bx + c = 0 are two consecutive integers, then b2 - 4c =1
Reason : If a, b, c are odd integer then the roots of the equation 4abc x2 + (b2 - 4ac)x - b = 0 are real and distinct.
- a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- c)Assertion (A) is true but reason (R) is false.
- d)Assertion (A) is false but reason (R) is true.
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
DIRECTION : In the following questions, a statement of assertion (A) i...
Assertion : Given equation
x2 - bx + c = 0
Let α,β be two roots such that
|α, - β|2 = 1
(α + β)2 - 4αβ = 1
b2 - 4c = 1
Reason : Given equation
4abc x2 + (b2- 4ac) x - b = 0
D = (b2 - 4ac)2 + 16ab2 c
D = (b2 - 4ac)2 > 0
Hence roots are real and unequal.
Most Upvoted Answer
DIRECTION : In the following questions, a statement of assertion (A) i...
Assertion : Given equation
x2 - bx + c = 0
Let α,β be two roots such that
|α, - β|2 = 1
(α + β)2 - 4αβ = 1
b2 - 4c = 1
Reason : Given equation
4abc x2 + (b2- 4ac) x - b = 0
D = (b2 - 4ac)2 + 16ab2 c
D = (b2 - 4ac)2 > 0
Hence roots are real and unequal.
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Community Answer
DIRECTION : In the following questions, a statement of assertion (A) i...
Assertion (A): If roots of the equation x2 - bx + c = 0 are two consecutive integers, then b2 - 4c = 1.
Reason (R): If a, b, c are odd integers, then the roots of the equation 4abc x2 + (b2 - 4ac)x - b = 0 are real and distinct.
Explanation:
To understand why option 'B' is the correct answer, let's analyze the assertion and reason separately.
Assertion (A): If roots of the equation x2 - bx + c = 0 are two consecutive integers, then b2 - 4c = 1.
To solve this, we can use the sum and product of roots formula for a quadratic equation. Let the roots of the given equation be p and p+1 (consecutive integers).
According to the sum of roots formula, p + (p+1) = -(-b) = b.
And according to the product of roots formula, p(p+1) = c.
Expanding the product, we get p^2 + p = c.
Substituting the value of b from the sum of roots formula, we get p^2 + p = b.
Rearranging the terms, p^2 + p - b = 0.
Comparing this with the general form of a quadratic equation ax^2 + bx + c = 0, we can see that a = 1, b = 1, and c = -b.
Now, using the discriminant formula, which is b^2 - 4ac, we can find the discriminant for the given equation.
Substituting the values, we get b^2 - 4ac = 1^2 - 4(1)(-b) = 1 + 4b = 4b + 1.
So, the assertion is true.
Reason (R): If a, b, c are odd integers, then the roots of the equation 4abc x^2 + (b^2 - 4ac)x - b = 0 are real and distinct.
To analyze this reason, we need to check if the discriminant of the equation 4abc x^2 + (b^2 - 4ac)x - b = 0 is positive or not.
Using the discriminant formula, which is b^2 - 4ac, we can find the discriminant for the given equation.
Substituting the values, we get (b^2 - 4ac) = (b^2 - 4(4abc)(-b)) = b^2 + 16ab^2c = b^2(1 + 16ac).
Since a, b, and c are odd integers, we can write them as a = 2k+1, b = 2l+1, and c = 2m+1, where k, l, and m are integers.
Substituting these values, we get (2l+1)^2(1 + 16(2k+1)(2m+1)) = (4l^2 + 4l + 1)(1 + 16(4km + 2k + 2m + 1)) = (4
Reason (R): If a, b, c are odd integers, then the roots of the equation 4abc x2 + (b2 - 4ac)x - b = 0 are real and distinct.
Explanation:
To understand why option 'B' is the correct answer, let's analyze the assertion and reason separately.
Assertion (A): If roots of the equation x2 - bx + c = 0 are two consecutive integers, then b2 - 4c = 1.
To solve this, we can use the sum and product of roots formula for a quadratic equation. Let the roots of the given equation be p and p+1 (consecutive integers).
According to the sum of roots formula, p + (p+1) = -(-b) = b.
And according to the product of roots formula, p(p+1) = c.
Expanding the product, we get p^2 + p = c.
Substituting the value of b from the sum of roots formula, we get p^2 + p = b.
Rearranging the terms, p^2 + p - b = 0.
Comparing this with the general form of a quadratic equation ax^2 + bx + c = 0, we can see that a = 1, b = 1, and c = -b.
Now, using the discriminant formula, which is b^2 - 4ac, we can find the discriminant for the given equation.
Substituting the values, we get b^2 - 4ac = 1^2 - 4(1)(-b) = 1 + 4b = 4b + 1.
So, the assertion is true.
Reason (R): If a, b, c are odd integers, then the roots of the equation 4abc x^2 + (b^2 - 4ac)x - b = 0 are real and distinct.
To analyze this reason, we need to check if the discriminant of the equation 4abc x^2 + (b^2 - 4ac)x - b = 0 is positive or not.
Using the discriminant formula, which is b^2 - 4ac, we can find the discriminant for the given equation.
Substituting the values, we get (b^2 - 4ac) = (b^2 - 4(4abc)(-b)) = b^2 + 16ab^2c = b^2(1 + 16ac).
Since a, b, and c are odd integers, we can write them as a = 2k+1, b = 2l+1, and c = 2m+1, where k, l, and m are integers.
Substituting these values, we get (2l+1)^2(1 + 16(2k+1)(2m+1)) = (4l^2 + 4l + 1)(1 + 16(4km + 2k + 2m + 1)) = (4
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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If roots of the equation x2 - bx + c = 0 are two consecutive integers, then b2 - 4c =1Reason : If a, b, c are odd integer then the roots of the equation 4abc x2 + (b2 - 4ac)x - b = 0 are real and distinct.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'B'. Can you explain this answer?
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DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If roots of the equation x2 - bx + c = 0 are two consecutive integers, then b2 - 4c =1Reason : If a, b, c are odd integer then the roots of the equation 4abc x2 + (b2 - 4ac)x - b = 0 are real and distinct.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'B'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If roots of the equation x2 - bx + c = 0 are two consecutive integers, then b2 - 4c =1Reason : If a, b, c are odd integer then the roots of the equation 4abc x2 + (b2 - 4ac)x - b = 0 are real and distinct.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If roots of the equation x2 - bx + c = 0 are two consecutive integers, then b2 - 4c =1Reason : If a, b, c are odd integer then the roots of the equation 4abc x2 + (b2 - 4ac)x - b = 0 are real and distinct.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'B'. Can you explain this answer?.
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If roots of the equation x2 - bx + c = 0 are two consecutive integers, then b2 - 4c =1Reason : If a, b, c are odd integer then the roots of the equation 4abc x2 + (b2 - 4ac)x - b = 0 are real and distinct.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'B'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If roots of the equation x2 - bx + c = 0 are two consecutive integers, then b2 - 4c =1Reason : If a, b, c are odd integer then the roots of the equation 4abc x2 + (b2 - 4ac)x - b = 0 are real and distinct.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If roots of the equation x2 - bx + c = 0 are two consecutive integers, then b2 - 4c =1Reason : If a, b, c are odd integer then the roots of the equation 4abc x2 + (b2 - 4ac)x - b = 0 are real and distinct.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'B'. Can you explain this answer?.
Solutions for DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If roots of the equation x2 - bx + c = 0 are two consecutive integers, then b2 - 4c =1Reason : If a, b, c are odd integer then the roots of the equation 4abc x2 + (b2 - 4ac)x - b = 0 are real and distinct.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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Here you can find the meaning of DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If roots of the equation x2 - bx + c = 0 are two consecutive integers, then b2 - 4c =1Reason : If a, b, c are odd integer then the roots of the equation 4abc x2 + (b2 - 4ac)x - b = 0 are real and distinct.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If roots of the equation x2 - bx + c = 0 are two consecutive integers, then b2 - 4c =1Reason : If a, b, c are odd integer then the roots of the equation 4abc x2 + (b2 - 4ac)x - b = 0 are real and distinct.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'B'. Can you explain this answer?, a detailed solution for DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If roots of the equation x2 - bx + c = 0 are two consecutive integers, then b2 - 4c =1Reason : If a, b, c are odd integer then the roots of the equation 4abc x2 + (b2 - 4ac)x - b = 0 are real and distinct.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If roots of the equation x2 - bx + c = 0 are two consecutive integers, then b2 - 4c =1Reason : If a, b, c are odd integer then the roots of the equation 4abc x2 + (b2 - 4ac)x - b = 0 are real and distinct.a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).c)Assertion (A) is true but reason (R) is false.d)Assertion (A) is false but reason (R) is true.Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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