Question 285939
{{{ax^2 + bx + c = 0}}}
{{{x^2 + (b/a)*x + (c/a) = 0}}}
If the roots are {{{r[1]}}} and {{{r[2]}}}
{{{(x - r[1])*(x - r[2]) = 0}}}
{{{x^2 - (r[1] + r[2])*x + r[1]*r[2] = 0}}}
Comparing the equations:
(1) {{{-(r[1] + r[2]) = b/a}}}
(2) {{{r[1]*r[2] = c/a}}}
I'll say
{{{r[01] = -(1/r[1])}}}
{{{r[02] = -(1/r[2])}}}
and
{{{r[1] = -(1/r[01])}}}
{{{r[2] = -(1/r[02])}}}
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from (2)
{{{(-1/r[01])*(-1/r[02]) = c/a}}}
{{{1/(r[01]*r[02]) = c/a}}}
{{{r[01]*r[02] = a/c}}}
from (1)
{{{-(-1/r[01] - 1/r[02]) = b/a}}}
{{{1/r[01] + 1/r[02] = b/a}}}
multiply both sides by {{{r[01]*r[02]}}}
{{{r[02] + r[01] = (b/a)*r[01]*r[02]}}}
{{{r[02] + r[01] = (b/a)*(a/c)}}}
{{{r[01] + r[02] = b/c}}}
and
{{{x^2 - (r[01] + r[02])*x + r[01]*r[02] = 0}}}
{{{x^2 - (b/c)*x + a/c = 0}}}
{{{cx^2 - bx + a = 0}}}
There could be a flaw somewhere -look it over