If `ax^2+2bx+c=0 and a_1x^2+2b_1x+c_1=0` have commonroot and `a/a_1,b/b_1,c/c_1` are in A.P., show that are: `ax^2+2bx+c=0`

If ax^2+2bx+c=0 and a_1x^2+2b_1x+c_1=0 have a common root and a/a_1,b/b_1,c/c_1 are in AP then a_1,b_1,c_1 are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If a^2+2bx+c=0 and a_1x^2+2b_1x+c_1=0 have a common root and a/a_1,b/b_1,c/c_1 are in AP then a_1,b_1,c_1 are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

If ax^2 + 2bx + c = 0 and x^2 + 2b_(1)x + c_(1) = 0 have a common root and a/a_(1), b/b_(1),c/c_(1) are in show that a_(1), b_(1), c_(1) are in G.P.

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

If the equations ax^(2) +2bx +c = 0 and Ax^(2) +2Bx+C=0 have a common root and a,b,c are in G.P prove that a/A , b/B, c/C are in H.P

If the equations ax^(2) +2bx +c = 0 and Ax^(2) +2Bx+C=0 have a common root and a,b,c are in G.P prove that a/A , b/B, c/C are in H.P

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

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.