If `a, b, c, x` are all real numbers, and `(a^2 + b^2)x^2 - 2b(a + c)x + (b^2 + c^2) = 0`, prove that `a,b, c` are in G.P., and `x` is their common ratio.

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

If a ,b ,c ,da n dp are distinct real numbers such that (a^2+b^2+c^2)p^2-2(a b+b c+c d)p+(b^2+c^2+d^2)lt=0, then prove that a ,b ,c , d are in G.P.

If a ,b ,c ,da n dp are distinct real numbers such that (a^2+b^2+c^2)p^2-2(a b+b c+c d)p+(b^2+c^2+d^2)lt=0, then prove that a ,b ,c , d 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 x, a, b, c are real and (x-a+b)^(2)+(x-b+c)^(2)=0 , then a, b, c are in

If x, a, b, c are real and (x-a+b)^(2)+(x-b+c)^(2)=0 , then a, b, c are in

IF x,a,b,c are real and (x-a+b^2)+(x-b+c)^2=0 then a,b,c are in

a ,b ,c are positive real numbers forming a G.P. If ax^2+2b x+c=0 and dx^2+2e x+f=0 have a common root, then prove that d//a ,e//b ,f//c are in A.P.

If a ,\ b ,\ c are real numbers, then find the intervals in which f(x)=|(x+a^2,a b, a c),( a b, x+b^2,b c),( a c, b c, x+c^2)| is increasing or decreasing.

a ,b ,c are positive real numbers forming a G.P. ILf a x^2+2b x+c=0a n ddx^2+2e x+f=0 have a common root, then prove that d//a ,e//b ,f//c are in A.P.