Physics: Spring Elastic Energy?

Question

A spring of negligible mass has force constant K= 1400.

Part A:

How far must the spring be compressed for an amount 3.20 of potential energy to be stored in it?

Part B:

You place the spring vertically with one end on the floor. You then drop a book of mass 1.20 onto it from a height of 0.700 above the top of the spring. Find the maximum distance the spring will be compressed.

Answer 1

a)PE=.5ks^2
3.2=.5(1400)s^2
s=.0676m
b)PE(gravity)=mgh
energy is conserved
mgh=.5ks^2
(1.2)(9.8)(.7+s)=.5(1400)s^2
0=700s^2-11.76s-8.232
quadratic formula...
s=.117 or -.1
cant be negative...
s=.117m