Multiple choice

If (1 – p) is a root of quadratic equation x2 + px + (1 – p) = 0, then its other roots are

  1. 0, 1

  2. – 1, 1

  3. 0, – 1

  4. – 1, 2
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C Correct answer
AI explanation

Because (1 - p) is a root of x^2 + px + (1 - p) = 0, we substitute x = 1 - p into the equation to get (1 - p)^2 + p(1 - p) + (1 - p) = 0. Factoring out (1 - p) from the first two terms yields (1 - p)[(1 - p) + p] + (1 - p) = 0, which simplifies to (1 - p)(1) + (1 - p) = 2(1 - p) = 0, meaning p = 1. Substituting p = 1 back into the original quadratic equation results in x^2 + x = 0, which factors as x(x + 1) = 0, giving roots of 0 and -1.

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