UGC NET Questions (Paper – 1)

For a quadratic equation ax² + bx + c = 0, the sum of the roots is given by −b/a. In the given equation, a = 1 and b = −5, so the sum of the roots is −(−5)/1 = 5. Thus, the correct sum of the roots is 5.

Option A:
A value of 6 is actually the product of the roots for this quadratic, given by c/a = 6/1 = 6. This represents a different relationship between coefficients and roots. Since the question specifically asks for the sum of the roots, 6 is not the correct answer.

Option B:
4 does not correspond to either the sum or product derived from the standard formulas for this equation. It might result from a miscalculation when solving the quadratic. Therefore, 4 cannot be justified as the sum of the roots.

Option C:
5 is correct because it directly results from applying the formula −b/a with b = −5 and a = 1. If we factor the equation as (x−2)(x−3) = 0, the roots are 2 and 3, whose sum is also 5, confirming the calculation. This dual reasoning strengthens the validity of option C.

Option D:
2 is one of the roots of the equation but not the sum of both roots. Confusing a single root with the sum of all roots leads to this incorrect choice. Thus, 2 cannot satisfy the requirement of adding both roots together.