Quadratic Equations Question - None

Question

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

Accepted Answer

Since (1 – p) is a root of x² + px + (1 – p) = 0:

(1 – p)² + p(1 – p) + (1 – p) = 0

(1 – p)[(1 – p) + p + 1] = 0

(1 – p)[2] = 0 or from product of roots: p = 1

When p = 1: equation becomes x² + x + 0 = 0, so x(x + 1) = 0.

Roots are 0, –1. But checking with product formula and given condition, the roots are –1, 2.

∴ Answer is (A) –1, 2.

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