If ` ax^2+2bx+c=0` , `a_1x^2+2b_1x+c_1=0` have a common root then the roots of the equation `(b^2-ac)x^2+(2 b b_1-ac_1-a_1c)x+(b_1^2-a_1c_1)=0` are

If a lt c lt b then the roots of the equation (a−b)x^2 +2(a+b−2c)x+1=0 are

If x^(2)+ax+bc=0 and x^(2)+bx+ca=0 have a common root,then a+b+c=1

If a_1x^2 + b_1 x + c_1 = 0 and a_2x^2 + b_2 x + c_2 = 0 has a common root, then the common root 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 a,b,c, a_1,b_1,c_1 are rational and equations ax^2+2bx+c=0 and a_1x^2+2b_1x+c_1=0 have one and only one root in common, prove that b^2-ac and b_1^2-a_1c_1 must be perfect squares.

If a,b,c, a_1,b_1,c_1 are rational and equations ax^2+2bx+c=0 and a_1x^2+2b_1x+c_1=0 have one and only one root in common, prove that b^2-ac and b_1^2-a_1c_1 must be perfect squares.

If a_(1)x^(2)+b_(1)x+c_(1)=0 and a_(2)x^(2)+b_(2)x+c_(2)=0 has a common root,then the common root is

If the equation ax^(2)+2bx+c=0 and x^(2)+2p^(2)x+1=0 have one common root and a,b,c are in AP(p^(2)!=1), then the roots of the equation x^(2)+2p^(2)x+1=0 are

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