Question 1050824
p AND q are the two roots



{{{x=(-1+- sqrt(1-4*q))/2}}}


{{{system(x=(-1-sqrt(1-4q))/2,  or, x=(-1+sqrt(1-4q))/2)}}}


(A)
p=-1,q=0


{{{x^2+x=0}}}

{{{x(x+1)=0}}}

Which conditions true?
No problems and no conflicts.  Many things may be true.  p and q are real roots.  Discriminant is greater than 0, as in {{{1^2-4*1*0=1}}}.


(B)
p=1,q=-2

You can try the substitution and look for something similar in method as in A.
{{{(x-1)(x+2)=0}}}
and simplifying and finding discriminant, this would be also greater than 0.


Using the general solution formula was not necessary.  Factorizations were possible.