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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
879 Points
11 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..

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Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

paradox xyz cool
29 Points
11 years ago

 how??? plz explain

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