If n is a root of the equation x² + px + m = 0 and m is a root of the equation x² + px + n = 0, where m ≠ n, then what is the value of p + m + n?

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Question

This question was previously asked in

NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)

Answer 1

Calculation:

Given,

n is a root of the equation $x^2 + px + m = 0$

⇒ $n^2 + pn + m = 0$ ..... (1)

Also, m is the root of equation of x2 + px + n = 0

⇒ $m^2 +pm+ n =0$ ..... (2)

Now Eq. (i) – Eq. (ii), we get

⇒ $(n^2 – m^2) + p(n – m) – (n – m) = 0$

⇒ $(n – m) [(n + m) + p – 1] = 0$

⇒ $n + m + p – 1 = 0$ ..... ( n ≠ m)

⇒ n + m + p = 1

∴ Option (c) is correct.

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