NDA Mathematics Question (2026) — Solution

Step-by-step solution

Let the quadratic equation be x^2 + px + q = 0. Let its roots be and . Sum of roots: + = -p Product of roots: = q The roots of the new equation are ^2 and ^2. Sum of new roots: ^2 + ^2 = ( + )^2 - 2 = p^2 - 2q Product of new roots: ^2 ^2 = q^2 Since the equation remains unchanged, the sum and product of the roots must be the same as the original equation. Therefore, p^2 - 2q = -p and q^2 = q. From q^2 = q, we get q = 0 or q = 1. Case 1: q = 0 Substituting q = 0 in p^2 - 2q = -p, we get p^2 = -p p^2 + p = 0 p(p + 1) = 0. This gives p = 0 or p = -1. The corresponding equations are x^2 = 0 and x^2 - x = 0. Case 2: q = 1 Substituting q = 1 in p^2 - 2q = -p, we get p^2 - 2 = -p p^2 + p - 2 = 0 (p + 2)(p - 1) = 0. This gives p = -2 or p = 1. The corresponding equations are x^2 - 2x + 1 = 0 and x^2 + x + 1 = 0. Thus, there are 4 such quadratic equations. Answer: 4