What is the value of b in the quadratic equation 4x^2 + bx + 12 =0 so that one root is thrice the other.

To find the value of b in 4x^2+bx+12 = 0, given that one
root is 3 times the other.

Let  a and 3a be the
roots.

Therefore by the relation between the roots and
coeficients, we have

a+3a = -b/4
.Or

 4a =
-b/12...............(1)

a*3a = 12/4.
Or

a^2 = 
1.................(2).

Eliminate a between (1) and (2)
:

(-b/12*4)^2 = 1.

b^2/48^2 =
1

 b^2 = 48^2

 We take square
root:

b = 48

b =
-48

Therefore the values of b  are  96 or
-96.