Prove that equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 have equal roots, show that roots are equal

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if the roots of the quadratic equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are equal show that a=b=c if the roots of the quadratic equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are equal show that a=b=c
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