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Grade 11Algebra

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)

Profile image of Anand Rananaware
15 Years agoGrade 11
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1 Answer

Profile image of SAGAR SINGH - IIT DELHI
15 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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