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 (aa_(1)-cc_(1))^(2)=(bc_(1)-ab_(1))(b_(1)c-a_(1)b)

If a root of the equation ax^(2)+bx+c=0 be reciprocal of a root of the equation a'x^(2)+b'x+c'=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

The roots of a quadratic equation ax^(2) + bx + c=0 are 1 and c/a , then a + b = "_____" .

if the roots of the equation (x-a)/(ax-1)=(x-b)/(bx+1) are reciprocal to each other.then a.a=1 b.b=2 c.a=2b d.b=0

If alpha,beta are the roots of the equations ax^(2)+bx+c=0 then the roots of the equation a(2x+1)^(2)+b(2x+1)(x-1)+c(x-1)^(2)=0

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