Show that one of the roots of equation `ax^2+bx+c=0` may be reciprocal of one of the roots of `a_1x^2+b_1x+c_1=0 if (aa_1-c``c_1)^2=(bc_1-ab_1)(b_1c-a_1b)`

If one of the roots of the equation ax^2 + bx + c = 0 be reciprocal of one of the a_1 x^2 + b_1 x + c_1 = 0 , then prove that (a a_1-c c_1)^2 =(bc_1-ab_1) (b_1c-a_1 b) .

If one of the roots of the equation ax^(2)+bx+c=0 be reciprocal of one of the a_(1)x^(2)+b_(1)x+c_(1)=0, then prove that (aa_(1)-cc_(1))^(2)=(bc_(1)-ab_(1))(b_(1)c-a_(1)b)

The condition that a root of ax^2+bx +c=0 may be the reciprocal of a root of a_1 x^2+b_1x +c_1=0 is

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

If one of the roots of the equation a(b-c)x^(2)+b(c-a)x+c(a-b)=0 is 1, the other root is

if one of the root of the equation a(b-c)x^(2)+b(c-a)x+c(a-b)=0 is 1,the other root is

If one root of the equation ax^(2) + bx + c =0 is reciprocal of the one root of the equation a_(1)x^(2) + b_(1) x + c_(1) = 0 , then :

The roots of a_(1)x^(2)+b_(1)x+c_(1)=0 are reciprocal of the roots of the equation a_(2)x^(2)+b_(2)x+c_(2)=0 if

If the ratio of the roots of the equation ax^2+bx+c=0 is equal to ratio of roots of the equation x^2+x+1=0 then a,b,c are in

If the ratio of the roots of the equation ax^(2)+bx+c=0 is equal to ratio of roots of the equation x^(2)+x+1=0 then a,b,c are in