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What is the positive value of m for which the roots of the equation 12x2 + mx + 5 = 0 are in the ratio 3 ∶ 2?
- a)5 √10
- b)5 √10/12
- c)5/12
- d)12/5
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
What is the positive value of m for which the roots of the equation 12...
Let the roots be 3t and 2t respectively
Product of the roots = c/a
3t × 2t = 5/12
t2 = 5/72
∴ t = ± √5/(6√2)
Sum of roots = -b/a
3t + 2t = -m/12
-60t = m
∴ m = -60 × ± √5/(6√2) = ± 5√10
Only positive value of m is required
∴ m = 5√10
Product of the roots = c/a
3t × 2t = 5/12
t2 = 5/72
∴ t = ± √5/(6√2)
Sum of roots = -b/a
3t + 2t = -m/12
-60t = m
∴ m = -60 × ± √5/(6√2) = ± 5√10
Only positive value of m is required
∴ m = 5√10
Most Upvoted Answer
What is the positive value of m for which the roots of the equation 12...
Let the roots of the equation be 3k and 2k, where k is a constant.
By Vieta's formulas, the sum of the roots is given by 3k + 2k = -m/12.
Simplifying, we have 5k = -m/12.
Since we want the roots to be in the ratio 3:2, we can set up the equation 3k/2k = 3/2.
Simplifying, we have 3/2 = 3/2.
Therefore, k = 1.
Substituting this back into the equation 5k = -m/12, we have 5 = -m/12.
Solving for m, we have m = -60.
Since we want the positive value of m, the answer is m = 60.
Therefore, the positive value of m for which the roots of the equation are in the ratio 3:2 is 60.
The correct answer is a) 60.
By Vieta's formulas, the sum of the roots is given by 3k + 2k = -m/12.
Simplifying, we have 5k = -m/12.
Since we want the roots to be in the ratio 3:2, we can set up the equation 3k/2k = 3/2.
Simplifying, we have 3/2 = 3/2.
Therefore, k = 1.
Substituting this back into the equation 5k = -m/12, we have 5 = -m/12.
Solving for m, we have m = -60.
Since we want the positive value of m, the answer is m = 60.
Therefore, the positive value of m for which the roots of the equation are in the ratio 3:2 is 60.
The correct answer is a) 60.
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What is the positive value of m for which the roots of the equation 12x2+ mx + 5 = 0 are in the ratio 3 2?a)5 √10b)5 √10/12c)5/12d)12/5Correct answer is option 'A'. Can you explain this answer?
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