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A value of b for which the equations x2 + bx - 1 = 0 x2 + x + b = 0, have one root in common is

A value of b for which the equations x2 + bx - 1 = 0 x2 + x + b = 0, have one root in common is

Grade:11

1 Answers

Vikas TU
14149 Points
one year ago
The given equation be as,x2+bx−1=0       .....(1)
x2+x+b=0         .....(2)
Let α be the common root. So, α satisfies both the equations.α2+bα−1=0       .....(3)
α2+α+b=0         .....(4)
Subtracting equation (3) and (4),
we have,α(b−1)−1−b=0
⇒α=1+b / b−1Substitute value of α in equation(3), we have, (1+b/ b−1)^2 + b(1+b / b−1) −1=0
⇒(1+b)^2+b(b^2−1)−(b−1)2=0
⇒  b3+3b=0⇒b(b2+3)=0
⇒b=0,±3−√i

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