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If the quadratic equation x² + px + (1 - p) = 0 has (1 - p) as one of its roots, what are the two roots of the equation?

1. -1, 2
2. -1, 1
3. 0, -1
4. 0, 1

Correct answer: 0, -1

Solution

Put x = (1-p) into x^2 + px + (1-p) = 0: (1-p)[(1-p)+p+1] = 2(1-p) = 0, so p = 1. The equation becomes x^2 + x = 0 -> x(x+1) = 0, giving roots 0 and -1.

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