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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 (A): If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.
Reason (R): If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.
- 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 'D'. Can you explain this answer?
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Verified Answer
Direction: In the following questions, a statement of assertion (A) i...
Let α and β be the roots of the quadratic polynomial. If α and β are positive then α + β = -b/a it it shows that -b/a is negative but sum of two positive numbers (α, β) must be +ve i.e., either b or a must be negative. So, a, b and c will have different signs.
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∴ Given statement is incorrect.
In case of reason:
Let β = 0, γ = 0
f(x) = (x – α) (x – β) (x – γ)
= (x – α) x · x
⇒ f(x) = x3 – αx2 which has no linear (coefficient of x) and constant terms.
∴ Given statement is correct.
Thus, assertion is incorrect but reason is correct.
Most Upvoted Answer
Direction: In the following questions, a statement of assertion (A) i...
Assertion and Reasoning
Assertion (A): If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.
Reason (R): If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.
Explanation
The assertion is false and the reason is true.
Explanation of Assertion (A): If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c may or may not have the same sign. For example, let's consider the quadratic polynomial x2 - 5x + 6. The zeroes of this polynomial are 2 and 3. Here, a = 1, b = -5, and c = 6. It can be observed that a and c have the same sign, but b has a different sign. Therefore, the assertion is false.
Explanation of Reason (R): If two of the zeroes of a cubic polynomial are zero, then it means that the cubic polynomial can be written as kx(x-p)(x-q), where k is a constant and p and q are the other two zeroes. Since the cubic polynomial has two zeroes as zero, it means that one of the factors is x, and the other factor must be (x-p)(x-q). Therefore, the cubic polynomial can be written as kx(x-p)(x-q) = kx3 - k(p+q)x2 + kpq x. Here, the linear term and constant term are both zero. Therefore, the reason is true.
Therefore, option (D) is the correct answer.
Assertion (A): If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.
Reason (R): If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.
Explanation
The assertion is false and the reason is true.
Explanation of Assertion (A): If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c may or may not have the same sign. For example, let's consider the quadratic polynomial x2 - 5x + 6. The zeroes of this polynomial are 2 and 3. Here, a = 1, b = -5, and c = 6. It can be observed that a and c have the same sign, but b has a different sign. Therefore, the assertion is false.
Explanation of Reason (R): If two of the zeroes of a cubic polynomial are zero, then it means that the cubic polynomial can be written as kx(x-p)(x-q), where k is a constant and p and q are the other two zeroes. Since the cubic polynomial has two zeroes as zero, it means that one of the factors is x, and the other factor must be (x-p)(x-q). Therefore, the cubic polynomial can be written as kx(x-p)(x-q) = kx3 - k(p+q)x2 + kpq x. Here, the linear term and constant term are both zero. Therefore, the reason is true.
Therefore, option (D) is the correct 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 (A): If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.Reason (R): If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.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 'D'. 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 (A): If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.Reason (R): If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.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 'D'. 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 (A): If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.Reason (R): If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.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 'D'. 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 (A): If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.Reason (R): If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.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 'D'. 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 (A): If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.Reason (R): If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.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 'D'. 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 (A): If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.Reason (R): If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.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 'D'. 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 (A): If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.Reason (R): If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.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 'D'. 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 (A): If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.Reason (R): If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.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 'D'. 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 (A): If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.Reason (R): If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.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 'D'. 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 (A): If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.Reason (R): If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.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 'D'. 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 (A): If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.Reason (R): If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.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 'D'. 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 (A): If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.Reason (R): If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.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 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion (A): If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.Reason (R): If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.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 'D'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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