Question

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

Answer 1

A quadratic equation has a double root if and only if its discriminant is 0. Here, the discriminant of 2x^2 + bx + 18 = 0 is b^2 - 4 x 2 x 18 = b^2 - 144.

so b^2 = 144. Then

Answer 2

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.