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If the ratio of the roots of the equation px2 + qx + r = 0 is a : b, then ab/(a + b)2 is
- a)p2/qr
- b)pr/q2
- c)q2/pr
- d)pq/r2
Correct answer is option 'B'. Can you explain this answer?
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If the ratio of the roots of the equation px2 + qx + r = 0 is a : b, t...
Let two roots be 1.is ak,2.is bk where k is constant then find the given condition
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If the ratio of the roots of the equation px2 + qx + r = 0 is a : b, t...
Explanation:
Ratio of roots:
- Let the roots of the equation px^2 + qx + r = 0 be α and β.
- According to the given information, the ratio of roots is a : b.
Sum and Product of roots:
- The sum of roots (α + β) = -q/p and the product of roots (αβ) = r/p.
Using the ratio of roots:
- From the ratio of roots (a : b), we can express the roots as α = aK and β = bK, where K is a constant.
- Therefore, the sum of roots becomes aK + bK = K(a + b) and the product of roots becomes abK^2.
Relation with coefficients:
- As per Vieta's formulas, the sum and product of roots are related to the coefficients of the quadratic equation as follows:
- Sum of roots: α + β = -q/p
- Product of roots: αβ = r/p
Equating the expressions:
- Equating the expressions derived from the ratio of roots and coefficients, we get:
- K(a + b) = -q/p
- abK^2 = r/p
Finding the required expression:
- To find ab/(a + b)^2, we need to simplify abK^2 / (a + b)^2.
- Substituting the values of K from the first equation and simplifying, we get pr/q^2.
Therefore, the correct expression is pr/q^2 (option B).
Ratio of roots:
- Let the roots of the equation px^2 + qx + r = 0 be α and β.
- According to the given information, the ratio of roots is a : b.
Sum and Product of roots:
- The sum of roots (α + β) = -q/p and the product of roots (αβ) = r/p.
Using the ratio of roots:
- From the ratio of roots (a : b), we can express the roots as α = aK and β = bK, where K is a constant.
- Therefore, the sum of roots becomes aK + bK = K(a + b) and the product of roots becomes abK^2.
Relation with coefficients:
- As per Vieta's formulas, the sum and product of roots are related to the coefficients of the quadratic equation as follows:
- Sum of roots: α + β = -q/p
- Product of roots: αβ = r/p
Equating the expressions:
- Equating the expressions derived from the ratio of roots and coefficients, we get:
- K(a + b) = -q/p
- abK^2 = r/p
Finding the required expression:
- To find ab/(a + b)^2, we need to simplify abK^2 / (a + b)^2.
- Substituting the values of K from the first equation and simplifying, we get pr/q^2.
Therefore, the correct expression is pr/q^2 (option B).
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If the ratio of the roots of the equation px2 + qx + r = 0 is a : b, then ab/(a + b)2isa)p2/qrb)pr/q2c)q2/prd)pq/r2Correct answer is option 'B'. Can you explain this answer? for 2025 is part of preparation. The Question and answers have been prepared according to the exam syllabus. Information about If the ratio of the roots of the equation px2 + qx + r = 0 is a : b, then ab/(a + b)2isa)p2/qrb)pr/q2c)q2/prd)pq/r2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the ratio of the roots of the equation px2 + qx + r = 0 is a : b, then ab/(a + b)2isa)p2/qrb)pr/q2c)q2/prd)pq/r2Correct answer is option 'B'. Can you explain this answer?.
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