The quadratic equation 2x^2 + bx + 18 = 0 has a double root. find all possible values of b.

When a quadratic equation ax^2+bx+c has a double root, the discriminant,
D=b^2-4ac=0
Here 
a=2,
b=b,
c=18
and 
D=b^2-4ac=b^2-4*2*18=0 
solve for b
b^2-144=0
=> b= ± sqrt(144)= ± 12

So in order that the given equation has double roots,  the possible values of b are ± 12.