Question 981978
Zero Product principle  (x-r)(x-s)=0 for roots r and s.  The two multiplied binomials will  (usually) give a quadratic trinomial.


Example,  #5:
roots or zeros  -3 and 15.
{{{(x-(-3))(x-15)=0}}}
{{{(x+3)(x-15)=0}}}
{{{x^2-12x-45=0}}}
{{{system(a=1,b=-12,c=-45)}}}


Examples like #7,9,10 can be used to obtain something for {{{a<>1}}}, because if a is nonzero, it will not affect the truth for {{{a(x-r)(a-s)=0}}}, for roots r and s.