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.
