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Question

If (1-b) is a root of the quadratic equation x2+bx+(1b)=0, then find the roots of the equation.


Solution

It is given that (1-b) is the root of equation
x2+bx+(1b)=0
Putting the value of x = (1-b) in the equation,
(1b)2+b(1b)+(1b)=0
(1b)(1b+b+1)=0
(1b)(2)=0
1b=0
b=1
Thus, the equation reduces to:
x2+x=0
x(x+1)=0
x=0,1
Thus, the roots are 0,-1.
 

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