if (1-p) is a zero of x^2+px+1-p then fond both the zeros
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Substituting x=1−p, we get
(1−p)
2
+p(1−p)+(1−p)=0
(1−p)(1−p+p+1)=0
Hence, p=1
Thus, x=0 is root of the equation.
Now, the equation changes to
x
2
+x=0
x(x+1)=0
x=0 and x=−1
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