If `(1-p)` is a root of quadratic equation `x^2+p x+(1-p)=0,` then find its roots.

Options

A. `-1, 2`
B. `-1, 1`
C. `0, -1`
D. 0, 1

Answer

C

Explanation

Since (1-p) is a root of the given equation.
`therefore" "(1-p)^(2) + p(1-p) + (1-p) = 0`
`rArr" "(1-p) {(1-p)+p+1} = 0 rArr 2 (1-p) = 0 rArr p = 1`
Substituting p = 1 in the given equation, we get
`x^(2) + x = 0 rArr x = 0, -1`
Hence, 0 and -1 are the roots of the given equation.