SOLUTION: Show that the equation (x-a)(x-b)+(x-b)(x-c)+(x-a)(x-c)=0 has equal roots when a=b=c

SOLUTION: Show that the equation (x-a)(x-b)+(x-b)(x-c)+(x-a)(x-c)=0 has equal roots when a=b=c

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Question 153004: Show that the equation (x-a)(x-b)+(x-b)(x-c)+(x-a)(x-c)=0 has equal roots when a=b=c
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Plug in and

FOIL

Combine like terms.

Factor the left side

Divide both sides by 3.

Take the square root of both sides.

Add "a" to both sides.

So the expression has a root of (with a multiplicity of 2) if
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