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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.

Grade:12

2 Answers

SAGAR SINGH - IIT DELHI
879 Points
10 years ago

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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Sagar Singh

B.Tech, IIT Delhi

jagdish singh singh
173 Points
10 years ago

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