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NDA 2025 Maths · Mathematics · Quadratic Equations · medium

If a quadratic with real coefficients has a non-real root, its conjugate is also a root. 2. If a quadratic with rational coefficients has the root…

Single correct option

Consider the following statements:
1. If a quadratic with real coefficients has a non-real root, its conjugate is also a root.
2. If a quadratic with rational coefficients has the root 2+32+\sqrt3, then 2−32-\sqrt3 is also a root.
Which of the statements is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (C) Both 1 and 2

Both are true. Statement 1 follows by conjugating az2+bz+c=0az^2+bz+c=0 with real a,b,ca,b,c. Statement 2 holds because irrational roots of a rational quadratic come in conjugate pairs: the sum of roots must be rational, forcing the other root to be 2−32-\sqrt3.
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Original question written in the NDA 2025 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake