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 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 :

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)

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)

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

If the origin lies in the acute angle between the lines a_1 x + b_1 y + c_1 = 0 and a_2 x + b_2 y + c_2 = 0 , then show that (a_1 a_2 + b_1 b_2) c_1 c_2 lt0 .

If the line a_1 x + b_1 y+ c_1 = 0 and a_2 x + b_2 y + c_2 = 0 cut the coordinate axes in concyclic points, prove that : a_1 a_2 = b_1 b_2 .

Statement-1: If the equations ax^2 + bx + c = 0 (a, b, c in R and a != 0) and 2x^2 + 7x+10=0 have a common root, then (2a+c)/b =2. Statement-2: If both roots of a_1 x^2 + b_1 x+c_1 = 0 and a_2 x^2 + b_2x + c_2 = 0 are same, then a_1/a_2=b_1/b_2=c_1/c_2. Given a_1,b_1,c_1,a_2,b_2,c_2 in R and a_1 a_2 != 0. (i) Statement I is true , Statement II is also true and Statement II is correct explanation of Statement I (ii)Statement I is true , Statement II is also true and Statement II is not correct explanation of Statement I (iii) Statement I is true , Statement II is False (iv) Statement I is False, Statement II is True

For two linear equations , a_1x + b_1y + c_1=0 and a_2x + b_2y + c_2 = 0 , the condition (a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2) is for.