[" If the roots of "(a^(2)+b^(2))x^(2)-2b(a+c)x+(b^(2)+c^(2))=0" are real and equal then "a,b,c" are in "],[[" 1) A.P."," 2) H.P."," 3) G.P."," 4) A.G.P."]]

If a,b,c,d, x are real and the roots of equation (a^2+b^2+c^2)x^2-2(ab+bc+cd)x+(b^2+c^2+d^2)=0 are real and equal then a,b,c,d are in (A) A.P (B) G.P. (C) H.P. (D) none of these

If a,b,c,d, x are real and the roots of equation (a^2+b^2+c^2)x^2-2(ab+bc+cd)x+(b^2+c^2+d^2)=0 are real and equal then a,b,c,d are in (A) A.P (B) G.P. (C) H.P. (D) none of these

If the quadratic equation a^(2)(b^(2) -c^(2)) x^(2) +b^(2) (c^(2) -a^(2)) x+c^(2) (a^(2) -b^(2)) =0 has real and equal roots, than a^(2) , b^(2) ,c^(2) are (1) A.P. (2) (G.P. (3) H.P. (4) A.G.P.

If the quadratic equation a^(2)(b^(2) -c^(2)) x^(2) +b^(2) (c^(2) -a^(2)) x+c^(2) (a^(2) -b^(2)) =0 has real and equal roots, than a^(2) , b^(2) ,c^(2) are (1) A.P. (2) (G.P. (3) H.P. (4) A.G.P.

Roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are real and equal, then (A) a+b+c!=0 (B) a,b,c are in H.P. (C) a,b,c are in H.P. (D) a,b,c are in G.P.

Roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are real and equal, then (A) a+b+c!=0 (B) a,b,c are in H.P. (C) a,b,c are in A.P. (D) a,b,c are in G.P.

If the roots of the equation x^2-2(a+b)x+a(a+2b+c)=0 be equal , prove that a,b, c are in G.P,

If a^(2),b^(2),c^(2) are in A.P. ,then show that b+c,c+a,a+b are in H.P.

If alpha,beta are the nonzero roots of ax^(2)+bx+c=0 and alpha^(2),beta^(2) are the roots of a^(2)x^(2)+b^(2)x^(2)+b^(2)x+c^(2)=0, then a,b,c are in a.G.P.b.H.P. C.A.P.d.none of these