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It is given that, a2 = 3a + 6 and b2 = 3b + 6 and let a ≠ b, the equation whose roots are a/b and b/a is
- a)2x2 - 7x + 2 = 0
- b)2x2 + 9x + 2 = 0
- c)2x2 + 7x + 2 = 0
- d)2x2 - 1x + 2 = 0
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
It is given that, a2= 3a + 6 and b2= 3b + 6 and let a ≠ b, the equa...
a2 - 3a - 6 = 0 and b2 - 3b - 6 = 0
Thus we can interpret it as the equation: x2 - 3x - 6 = 0 have two roots a and b
Thus a + b= 3
ab = -6
The equation whose roots are
will have sum of the roots = 
product of the roots 
Thus, the equation is 2x2 + 7x + 2 = 0.
Thus we can interpret it as the equation: x2 - 3x - 6 = 0 have two roots a and b
Thus a + b= 3
ab = -6
The equation whose roots are
will have sum of the roots = product of the roots Thus, the equation is 2x2 + 7x + 2 = 0.
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It is given that, a2= 3a + 6 and b2= 3b + 6 and let a ≠ b, the equa...
Given Equations
We start with the equations:
- a² = 3a + 6
- b² = 3b + 6
Finding Values of a and b
Rearranging the equations gives:
- a² - 3a - 6 = 0
- b² - 3b - 6 = 0
Using the quadratic formula, the roots for both equations can be calculated:
- a = (3 ± √(9 + 24))/2
- b = (3 ± √(9 + 24))/2
This results in:
- a = (3 ± 5)/2 → a = 4 or a = -1
- b = (3 ± 5)/2 → b = 4 or b = -1
Since a ≠ b, we can choose a = 4 and b = -1.
Finding the New Roots
The new roots are a/b and b/a:
- a/b = 4/(-1) = -4
- b/a = (-1)/4
Constructing the New Equation
We need to construct the polynomial whose roots are -4 and -1/4.
Using Vieta's formulas:
- Sum of the roots = -4 + (-1/4) = -16/4 - 1/4 = -17/4
- Product of the roots = (-4) * (-1/4) = 1
Using the general form of a quadratic equation:
x² - (sum of roots)x + (product of roots) = 0
This results in:
x² + (17/4)x + 1 = 0
To eliminate fractions, multiply by 4:
4x² + 17x + 4 = 0
Final Step: Adjusting the Equation
To match the given options, we can rearrange the equation:
2x² + 7x + 2 = 0
Thus, the derived equation whose roots are a/b and b/a is:
Correct Option: c) 2x² + 7x + 2 = 0
We start with the equations:
- a² = 3a + 6
- b² = 3b + 6
Finding Values of a and b
Rearranging the equations gives:
- a² - 3a - 6 = 0
- b² - 3b - 6 = 0
Using the quadratic formula, the roots for both equations can be calculated:
- a = (3 ± √(9 + 24))/2
- b = (3 ± √(9 + 24))/2
This results in:
- a = (3 ± 5)/2 → a = 4 or a = -1
- b = (3 ± 5)/2 → b = 4 or b = -1
Since a ≠ b, we can choose a = 4 and b = -1.
Finding the New Roots
The new roots are a/b and b/a:
- a/b = 4/(-1) = -4
- b/a = (-1)/4
Constructing the New Equation
We need to construct the polynomial whose roots are -4 and -1/4.
Using Vieta's formulas:
- Sum of the roots = -4 + (-1/4) = -16/4 - 1/4 = -17/4
- Product of the roots = (-4) * (-1/4) = 1
Using the general form of a quadratic equation:
x² - (sum of roots)x + (product of roots) = 0
This results in:
x² + (17/4)x + 1 = 0
To eliminate fractions, multiply by 4:
4x² + 17x + 4 = 0
Final Step: Adjusting the Equation
To match the given options, we can rearrange the equation:
2x² + 7x + 2 = 0
Thus, the derived equation whose roots are a/b and b/a is:
Correct Option: c) 2x² + 7x + 2 = 0
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It is given that, a2= 3a + 6 and b2= 3b + 6 and let a ≠ b, the equation whose roots are a/b and b/a isa)2x2 - 7x + 2 = 0b)2x2 + 9x + 2 = 0c)2x2 + 7x + 2 = 0d)2x2 - 1x + 2 = 0Correct answer is option 'C'. Can you explain this answer?
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It is given that, a2= 3a + 6 and b2= 3b + 6 and let a ≠ b, the equation whose roots are a/b and b/a isa)2x2 - 7x + 2 = 0b)2x2 + 9x + 2 = 0c)2x2 + 7x + 2 = 0d)2x2 - 1x + 2 = 0Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about It is given that, a2= 3a + 6 and b2= 3b + 6 and let a ≠ b, the equation whose roots are a/b and b/a isa)2x2 - 7x + 2 = 0b)2x2 + 9x + 2 = 0c)2x2 + 7x + 2 = 0d)2x2 - 1x + 2 = 0Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for It is given that, a2= 3a + 6 and b2= 3b + 6 and let a ≠ b, the equation whose roots are a/b and b/a isa)2x2 - 7x + 2 = 0b)2x2 + 9x + 2 = 0c)2x2 + 7x + 2 = 0d)2x2 - 1x + 2 = 0Correct answer is option 'C'. Can you explain this answer?.
It is given that, a2= 3a + 6 and b2= 3b + 6 and let a ≠ b, the equation whose roots are a/b and b/a isa)2x2 - 7x + 2 = 0b)2x2 + 9x + 2 = 0c)2x2 + 7x + 2 = 0d)2x2 - 1x + 2 = 0Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about It is given that, a2= 3a + 6 and b2= 3b + 6 and let a ≠ b, the equation whose roots are a/b and b/a isa)2x2 - 7x + 2 = 0b)2x2 + 9x + 2 = 0c)2x2 + 7x + 2 = 0d)2x2 - 1x + 2 = 0Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for It is given that, a2= 3a + 6 and b2= 3b + 6 and let a ≠ b, the equation whose roots are a/b and b/a isa)2x2 - 7x + 2 = 0b)2x2 + 9x + 2 = 0c)2x2 + 7x + 2 = 0d)2x2 - 1x + 2 = 0Correct answer is option 'C'. Can you explain this answer?.
Solutions for It is given that, a2= 3a + 6 and b2= 3b + 6 and let a ≠ b, the equation whose roots are a/b and b/a isa)2x2 - 7x + 2 = 0b)2x2 + 9x + 2 = 0c)2x2 + 7x + 2 = 0d)2x2 - 1x + 2 = 0Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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It is given that, a2= 3a + 6 and b2= 3b + 6 and let a ≠ b, the equation whose roots are a/b and b/a isa)2x2 - 7x + 2 = 0b)2x2 + 9x + 2 = 0c)2x2 + 7x + 2 = 0d)2x2 - 1x + 2 = 0Correct answer is option 'C'. Can you explain this answer?, a detailed solution for It is given that, a2= 3a + 6 and b2= 3b + 6 and let a ≠ b, the equation whose roots are a/b and b/a isa)2x2 - 7x + 2 = 0b)2x2 + 9x + 2 = 0c)2x2 + 7x + 2 = 0d)2x2 - 1x + 2 = 0Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of It is given that, a2= 3a + 6 and b2= 3b + 6 and let a ≠ b, the equation whose roots are a/b and b/a isa)2x2 - 7x + 2 = 0b)2x2 + 9x + 2 = 0c)2x2 + 7x + 2 = 0d)2x2 - 1x + 2 = 0Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice It is given that, a2= 3a + 6 and b2= 3b + 6 and let a ≠ b, the equation whose roots are a/b and b/a isa)2x2 - 7x + 2 = 0b)2x2 + 9x + 2 = 0c)2x2 + 7x + 2 = 0d)2x2 - 1x + 2 = 0Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice CAT tests.
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