Question 1026795
The roots are  x+4 and x-2p.


Zeros are x=-4 and x=2p.
The exact middle value between these zeros is  {{{(-4+2p)/2=p-2}}}.


Minimum value for {{{2(x+4)(x-2p)=-18}}} needs {{{x=p-2}}}.
{{{2(p-2+4)(p-2-2p)=-18}}}
{{{(p+2)(-p-2)=-9}}}
{{{(p+2)(p+2)=9}}}
{{{p+2=0+- 3}}}
{{{highlight(p=-2+- 3)}}}


p=1 or p=-5.