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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, x 2 +a 3 x+b 3 =0 hav exactly one root in comman , 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, x2+a3x+b3=0 hav exactly one root in comman , then show that


(a1+a2+a3) 2 = 4(a2a3+a3a1+a1a2-b1-b2-b3)


Grade:11

1 Answers

SAGAR SINGH - IIT DELHI
879 Points
11 years ago

Dear student,

Condition for common roots The equations a1X2 + b1X + c1 = 0 & a2 X2 + b2X + c2 = 0 have • a common roots if (c1 a2 − c2a1)2 = (b1 c2 − b2 c1) (a1 b2 − a2 b1).

 

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