Roots of the equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are equal then relation between a,b,c

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Show that the roots of the equation: (x-a) (x -b) +(x- b) (x-c)+ (x- c) (x -a) =0 are always rea... Show that the roots of the equation: (x-a) (x -b) +(x- b) (x-c)+ (x- c) (x -a) =0 are always rea...
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If a,b,cāˆˆR distinct, f(x)=a^2(x-a)(x-c)/(a-b)(a-c)+b^2(x-c)(x-a)/(b-c)(b-a)+ c^2(x-a)(x-b)/(c-a)(c-b If a,b,cāˆˆR distinct, f(x)=a^2(x-a)(x-c)/(a-b)(a-c)+b^2(x-c)(x-a)/(b-c)(b-a)+ c^2(x-a)(x-b)/(c-a)(c-b
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If the roots of the equation `(x-b)(x-c)+(x-c)(x-a)+(x-a)(x-b)=0` are equal then If the roots of the equation `(x-b)(x-c)+(x-c)(x-a)+(x-a)(x-b)=0` are equal then
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