Guest

If each pair of the following three equations: x 2 + a 1 x + b 1 = 0 , x 2 + a 2 x + b 2 = 0 and x 2 + a 3 x + b 3 = 0 has exactly one root in common, then show that ( a 1 + a 2 + a 3 ) 2 = 4( a 2 a 3 + a 3 a 1 + a 1 a 2 - b 1 - b 2 - b 3 ).

If each pair of the following three equations: x2 + a1x + b1 = 0 , x2 + a2x + b2 = 0 and x2 + a3x + b3 = 0 has exactly one root in common, then show that ( a1 + a2 + a3 )2 = 4( a2a3 + a3a1 + a1a2 - b1 - b2 - b3).

Grade:11

2 Answers

SAGAR SINGH - IIT DELHI
878 Points
13 years ago

Dear student,

Let us assume @ be the common root then it satisfies all these equations, so make use of this property to prove the equation in question..

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

paradox xyz cool
29 Points
13 years ago

 how??? plz explain

Think You Can Provide A Better Answer ?

ASK QUESTION

Get your questions answered by the expert for free