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Question

A real value of b for which the equations x2+bx1=0,x2+x+b=0 have one root in common is .....................

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Solution

If a1x2+b1x+c1=0 and a2x2+b2x+c2=0
have a common real root, then
(a1c2a2c1)2=(b1c2b2c1)(a1b2a2b1)
x2+bx1=0,x2+x+b=0 have a common root
(1+b)2=(b2+1)(1b)
b2+2b+1=b2b3+1b
b3+3b=0
b(b2+3)=0
b=0,±3i

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