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The quadratic equation whose roots are three times the roots of 3ax2 + 3bx + c = 0 is
- a)ax2 + 3bx + 3c = 0
- b)ax2 + 3bx + c = 0
- c)9ax2 + 9bx + c = 0
- d)ax2 + bx + 3c = 0
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The quadratic equation whose roots are three times the roots of 3ax2 +...
Solution:
Let the roots of the given equation 3ax2 + 3bx + c = 0 be α and β.
Then, α + β = -b/3a and αβ = c/3a.
Let the roots of the required equation ax2 + 3bx + 3c = 0 be kα and kβ.
Then, kα + kβ = -3b/a and kαkβ = 3c/a.
We know that the sum and product of roots of a quadratic equation are related to the coefficients of x2, x and constant term.
Therefore, we have:
k(α + β) = kα + kβ = -3b/a
=> k(-b/3a) = -3b/a
=> k = -9
And, kαkβ = 3c/a
=> (-9α)(-9β) = 3c/a
=> αβ = -c/27a
Substituting the value of αβ from the given equation, we get:
-c/27a = 3c/a
=> -c = 81c
=> c = 0
Therefore, the required equation is ax2 + 3bx + 3c = ax2 + 3bx + 0 = ax2 + 3bx, which is option A.
Let the roots of the given equation 3ax2 + 3bx + c = 0 be α and β.
Then, α + β = -b/3a and αβ = c/3a.
Let the roots of the required equation ax2 + 3bx + 3c = 0 be kα and kβ.
Then, kα + kβ = -3b/a and kαkβ = 3c/a.
We know that the sum and product of roots of a quadratic equation are related to the coefficients of x2, x and constant term.
Therefore, we have:
k(α + β) = kα + kβ = -3b/a
=> k(-b/3a) = -3b/a
=> k = -9
And, kαkβ = 3c/a
=> (-9α)(-9β) = 3c/a
=> αβ = -c/27a
Substituting the value of αβ from the given equation, we get:
-c/27a = 3c/a
=> -c = 81c
=> c = 0
Therefore, the required equation is ax2 + 3bx + 3c = ax2 + 3bx + 0 = ax2 + 3bx, which is option A.
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The quadratic equation whose roots are three times the roots of 3ax2 +...
Substitute x as x/3
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The quadratic equation whose roots are three times the roots of 3ax2 + 3bx + c = 0 isa)ax2 + 3bx + 3c = 0b)ax2 + 3bx + c = 0c)9ax2 + 9bx + c = 0d)ax2 + bx + 3c = 0Correct answer is option 'A'. Can you explain this answer?
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The quadratic equation whose roots are three times the roots of 3ax2 + 3bx + c = 0 isa)ax2 + 3bx + 3c = 0b)ax2 + 3bx + c = 0c)9ax2 + 9bx + c = 0d)ax2 + bx + 3c = 0Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The quadratic equation whose roots are three times the roots of 3ax2 + 3bx + c = 0 isa)ax2 + 3bx + 3c = 0b)ax2 + 3bx + c = 0c)9ax2 + 9bx + c = 0d)ax2 + bx + 3c = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The quadratic equation whose roots are three times the roots of 3ax2 + 3bx + c = 0 isa)ax2 + 3bx + 3c = 0b)ax2 + 3bx + c = 0c)9ax2 + 9bx + c = 0d)ax2 + bx + 3c = 0Correct answer is option 'A'. Can you explain this answer?.
The quadratic equation whose roots are three times the roots of 3ax2 + 3bx + c = 0 isa)ax2 + 3bx + 3c = 0b)ax2 + 3bx + c = 0c)9ax2 + 9bx + c = 0d)ax2 + bx + 3c = 0Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The quadratic equation whose roots are three times the roots of 3ax2 + 3bx + c = 0 isa)ax2 + 3bx + 3c = 0b)ax2 + 3bx + c = 0c)9ax2 + 9bx + c = 0d)ax2 + bx + 3c = 0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The quadratic equation whose roots are three times the roots of 3ax2 + 3bx + c = 0 isa)ax2 + 3bx + 3c = 0b)ax2 + 3bx + c = 0c)9ax2 + 9bx + c = 0d)ax2 + bx + 3c = 0Correct answer is option 'A'. Can you explain this answer?.
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