ANSWER
[tex] \boxed {b = \pm12}[/tex]
EXPLANATION
The given quadratic equation is
[tex]2 {x}^{2} + bx + 18 = 0[/tex]
By comparing to
[tex]a {x}^{2} +b x + 18 = 0[/tex]
[tex]a=2,c=18[/tex]
If this equation has a double root, then the discriminant is zero.
Thus,
[tex]{b}^{2} - 4ac = 0[/tex]
We substitute the values into the formula to obtain,
[tex] {b}^{2} - 4(2)(18) = 0[/tex]
[tex]\Rightarrow \: {b}^{2} - 144 = 0[/tex]
[tex]\Rightarrow \: {b}^{2} = 144 [/tex]
We take the square root of both sides to obtain,
[tex]b= \pm \: \sqrt{144} [/tex]
[tex]\Rightarrow \: b= \pm 12[/tex]
