Question 1058234
(1) {{{ a*x^2 + b*x + c = 0 }}}
Divide both sides by {{{ a }}}
{{{ x^2 + (b/a)*x + c/a = 0 }}}
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Roots are {{{ x[1] }}}, and {{{ x[2] }}}
{{{ ( x - x[1] )*( x - x[2] ) = x^2 - x[1]*x - x[2]*x + x[1]*x[2] = 0 }}}
(2) {{{ ( x - x[1] )*( x - x[2] ) = x^2 - ( x[1] + x[2] )*x + x[1]*x[2] = 0 }}}
Comparing (1) and (2),
{{{ x[1] + x[2] = -b/a }}}
{{{ x[1]*x[2] = c/a }}}