" Q."5" if roots of euqation "(a-b)x^(2)+(b-c)x+(c-a)=0" are equal,prove that "2b=a+c

If roots of equation a-b)x^(2)+(b-c)x+(c-a)=0 are equal then prove that b+c=2a

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

If the roots of the equation (b-c)x^(2)+(c-a)x+(a-b)=0 are equal,then prove that 2b=a+c

If the roots of the quadratic equation (a-b) x^(2) + (b - c) x + (c - a) =0 are equal , prove that b +c = 2a

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

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal, then prove that 2b=a+c

If the roots of (a-b)x^(2)+(b-c)x+(c-a)=0 are real and equal, then prove that b, a, c are in arithmetic progression.

If the roots of the equations (b-c) x^(2) + (c-a) x+( a-b) =0 are equal , then prove that 2b=a+c

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