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.