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

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Write the roots of the equation `(a-b)x^2+(b-c)x+(c-a)=0.` Write the roots of the equation `(a-b)x^2+(b-c)x+(c-a)=0.`
If the roots of the equation (a-b)x^2+(b-c)x+(c-a)=0 are equal prove that 2a=b+c If the roots of the equation (a-b)x^2+(b-c)x+(c-a)=0 are equal prove that 2a=b+c
If the roots of the equation (a-b)x 2 +(b-c)x+(c-a) =0 then prove that 2a=b+c If the roots of the equation (a-b)x 2 +(b-c)x+(c-a) =0 then prove that 2a=b+c
If the roots of the equation(a-b)x²+(b-c)x+(c-a)=0 then prove that 2a=b+c If the roots of the equation(a-b)x²+(b-c)x+(c-a)=0 then prove that 2a=b+c
If the roots of equation `a(b-c)x^2+b(c-a)x+c(a-b)=0` be equal prove that `a,b,c` are in H.P. If the roots of equation `a(b-c)x^2+b(c-a)x+c(a-b)=0` be equal prove that `a,b,c` are in H.P.
If the roots of the equation (a-b)x^2 +(b-c)x+(c-a) =0 then prove that b+c=2a If the roots of the equation (a-b)x^2 +(b-c)x+(c-a) =0 then prove that b+c=2a
Q. If the roots of the equation (a-b)x²+(b-c)x+(c-a)=0 are equal then prove that 2a=b+c. Q. If the roots of the equation (a-b)x²+(b-c)x+(c-a)=0 are equal then 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 equation (b-c)x^2+(c-a)x+(a-b)=0 are equal, then prove that 2b=a+c.