Guest

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
878 Points
13 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.

 

Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.

All the best.

Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar  respectively : Click here to download the toolbar..

 

Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

jagdish singh singh
173 Points
13 years ago

1472_24699_gif.latex (28).gif

Think You Can Provide A Better Answer ?

ASK QUESTION

Get your questions answered by the expert for free