Prove that the roots of the equation (x-a)(x-b)+(x-b)(x-c)+(x-a)(x-c)=0 are real.
Prove that the roots of the equation (x-a)(x-b)+(x-b)(x-c)+(x-a)(x-c)=0 are real.
Aparna Tiwari , 15 Years ago
Grade 12
Algebra> Quadratic Equations...
2 Answers
SAGAR SINGH - IIT DELHI
Dear aparna,
If we solve this equation we get,
3x2-2x(a+b+c)+ab+bc+ca=0
If we calculate discriminant D=b2-4ac
we find that D>0 hence the roots are real
Proved.
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