Question 981552
This response deals with your second question.
If 1-p is a root, then you must be asking what is the other root for {{{x^2+px+(1-p)=0}}}.


More than one way to go, but,
{{{x=(-p+- sqrt(p^2-4*(1-p)))/2}}}, using general formula for solution to a quadratic equation.


{{{x=(-p+- sqrt(p^2-4+4p))/2}}}


{{{x=(-p+- sqrt(p^2+4p-4))/2}}}----------these would be the roots!


You were expecting that 1-p is one of the roots.  Check if it really is a root.
{{{(1-p)^2+p(1-p)+(1-p)}}}
{{{1-2p+p^2+p-p^2+1-p}}}
{{{1+1-2p+p-p+p^2-p^2}}}
{{{2-2p=0}}}------Not true, because this depends on the value of p.


Your question or description for your exercise 2 is faulty.