Answer:
k = 9/8
Step-by-step explanation:
For a root with multiplicity 2, the discriminant must be zero. For quadratic ax^2 +bx +c, the discriminant is ...
d = b^2 -4ac
For your quadratic, a=2, b=3, c=k, so you want ...
3^2 -4(2)(k) = 0
9 -8k = 0
k = 9/8
