Introduction to the function

Question

Let f(x) =(x+3)(x+2). If f(2k)-f(k-1)=8, find the values of k.

Answer 1

f(2k)=(2k+3)(2k+2)=4k²+10k+6

f(k-1)=((k-1)+3)((k-1)+2)=(k+2)(k+1)=k²+3k+2

f(2k)-f(k-1)=3k²+7k+4=8

3k²+7k-4=0

k=(-7±sqrt(49+48))/6 by the quadratic formula

k=0.4748 or 2.808