Question 280070
The roots are the values of {{{x}}} that make
the equation true.
{{{ax^2 + bx + c = 0}}}
The quadratic formula for the roots is:
 {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
So, the 2 roots are:
 {{{x[1] = (-b + sqrt( b^2-4*a*c ))/(2*a) }}}
 {{{x[2] = (-b - sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x[1] + x[2] = -b/(2a) - b/(2a) }}}
{{{x[1] + x[2] = -b/a}}}
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Another way to do it is:
{{{ax^2 + bx + c = 0}}}
{{{x^2 + (b/a)*x + c/a = 0}}}
Call the roots {{{r[1]}}} and {{{r[2]}}}, then
{{{(x - r[1])*(x - r[2]) = 0}}}
{{{x^2 - (r[1] + r[2])*x + r[1]*r[2] = 0}}}
{{{-(r[1] + r[2]) = b/a}}}
{{{r[1] + r[2] = -b/a}}}