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?

Question

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 &radic;10b)5 &radic;10/12c)5/12d)12/5Correct answer is option 'A'. Can you explain this answer?

Answer

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.

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