Sum of Roots from Factorized Equation – UGC NET Question

The equation (x − 3)(x + 5) = 0 is satisfied when either factor is zero. Setting x − 3 = 0 gives x = 3, and setting x + 5 = 0 gives x = −5. The sum of the roots is therefore 3 + (−5) = −2. This also agrees with the general property that for x² + bx + c = 0, the sum of the roots is −b, which is consistent if the equation is expanded.

Option A:
Option A correctly adds the two root values, 3 and −5, to obtain −2. It captures the essence of the relationship between factorized form and the numerical roots.

Option B:
Option B, 2, would arise if one mistakenly subtracted −5 from 3 or ignored the sign of one root, but that does not reflect the actual arithmetic.

Option C:
Option C, −8, is the product of the roots, not their sum. It reflects a different relation in quadratics and confuses two separate concepts.

Option D:
Option D, 8, would require both roots to be positive or both negative with different magnitudes, which is not the case for this factorization.