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04 Jul 2022 Algebra

For the equation 10x² + kx + 6 = 0, if roots are in the ratio 3:4, then find positive value of k.

OPtion

1) 5√7
2) 2√5
3) 3√4
4) 7√5
5) 2√3
6) 7√10
7) 5√3
8) 7√3
9) 5√5
10) None of these

Solution

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

Correct Option: 4 Best Solution (0)