The roots of a1x^2+b1x + c1=0are recipro...

The roots of `a_1x^2+b_1x + c_1=0`are reciprocal of the roots of the equation `a_2x^2 +b_2x+c_2=0` if

`(a_(1)a _(2) -c_(1) c _(2)) ^(2) =(a_(1) b _(2) -b_(2) c _(2)) (a_(2) b _(1) -b_(2) c _(1))`

`(a_(1)a_(2) -_(1)b_(2)) ^(2) = (a _(2)b_(2)-b_(1)c _(2)) (a_(2) b _(1) - b _(2) c _(1))`

`(b_(1)c_(2) -b_(2)c_(1)) ^(2) = (a_(1)b_(2) +b_(1) c _(2)) (a_(2)b_(1) -b _(2) c _(1)) `

`(b_(1) c _(2) -b_(2) c_(1))^(2) = (a _(1)b_(2)+b_(1) c _(2)) (a_(1)b_(1) =b_(2)c _(1))`

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