Given equation: 10x² + kx + 6 = 0
The roots are in the ratio 3:4. Let roots of the equation are 3ɑ and 4ɑ.
Applying condition for sum and product of the roots,
Sum of roots = 3ɑ + 4ɑ = -k/10 ---(i) and
Product of roots = 3ɑ*4ɑ = 6/10 = 3/5
12ɑ² = 3/5
ɑ = ±1/(2√5)
From (i), k = -70ɑ
.'. k = -70*(-1/(2√5)) = 7√5