The positive value of m for which the roots of the equation

The positive value of m for which the roots of the equation 12x² + mx + 5 = 0 are in the ratio 3 : 2 is :

According to question , we can say that
Let, the roots be 3α and 2α .

Then, 3α + 2α =	m	⇒ α =	m
	12		60

∴	5	=		m		²	⇔	5	=	m²
	72			60				72		3600

⇔ m² =	3600 x 5	= 250
	72

∴ m = √250 = 5√10.
Thus , The positive value of m is 5√10.

5	√10
2