Q . the value of 'b' for which equations

x2+bx-1=0

x2+x+b=0

have one root in common is ??

The given equation be as,x2+bx-1=0       .....1x2+x+b=0         .....2Let α be the common root. So, α satisfies both the equations.α2+bα-1=0       .....3α2+α+b=0         .....4Subtracting equation 3 and 4, we have,αb-1-1-b=0α=1+bb-1Substitute value of α in equation3, we have, 1+bb-12+b1+bb-1-1=01+b2+bb2-1-b-12=0  b3+3b=0bb2+3=0b=0,±3i

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