Question 1073525
Starting with {{{x^2+bx+c=0}}}, and assigning roots as p and q,  and working with the roots from use of quadratic formula,


{{{system(p+q=-b,pq=c)}}}



If p and q are to be roots for {{{x^2+px+q=0}}} then this system should be possible:



{{{system(p+q=-p,pq=q)}}}


The second of these means p=1; and substituting into the first of these gives a way to solve for q.
{{{highlight(system(p=1,q=-2))}}}