Word Problem on Quadratic Equation

Topic : Quadratic Equation
Question : Determine the values of ‘K’ in the equation for which one root is triple the other root.
3x² + Kx + 4 = 0

Solution :
3x² + Kx + 4 = 0
Divide by 3
x² + (K/3)x + 4/3 = 0

Sum of roots = -K/3
Products of roots = 4/3
Let one root be x
So another root will be 3x (given)
X + 3x = -K/3
4x = -K/3

x(3x) =4/3
x² = 4/9
x = ±3/2

when x = 3/2

4(3/2) = -K/3
2(3)=-K/3
Multiply both sides by 3
18 = -K
So K = -18

When x = -3/2
4(-3/2)=-K/3
Negative sign get cancelled on both the sides
So we get, 2(3)=K/3
Multiply both sides by 318 = K