Question 707659
{{{ax^2 + bx + c = 0}}}....factor {{{x}}}

{{{x(ax+b) + c = 0}}}

assume {{{a}}},{{{b}}},{{{c}}} are all {{{odd}}}, then for this {{{to}}}{{{ have}}} a solution, {{{x(ax+b)}}} must be {{{odd}}} as {{{well}}}

however,

if {{{x}}} is {{{odd}}}, {{{ax+b}}} is {{{even}}}; so, {{{x(ax+b)}}} is {{{even}}}



so, if {{{a}}},{{{b}}},{{{c}}} are all {{{odd}}}, there are {{{no}}}{{{ possible}}}{{{ solutions}}}, the equation {{{ax^2+bx+c=0}}} has {{{no}}}{{{ rational}}}{{{ roots}}}