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NDA 2023 Maths · Mathematics · Quadratic Equations · medium

If a+b+c=0, then x=1 is a root of ax^2+bx+c=0. 2. A quadratic equation with irrational coefficients cannot have a rational root.

Single correct option

Consider the following statements:
1. If a+b+c=0a+b+c=0, then x=1x=1 is a root of ax2+bx+c=0ax^2+bx+c=0.
2. A quadratic equation with irrational coefficients cannot have a rational root.
Which of the statements given above 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: (A) 1 only

Statement 1 is correct because substituting x=1x=1 gives a+b+c=0a+b+c=0. Statement 2 is incorrect: 2x2−22x=0\sqrt2x^2-2\sqrt2x=0 has irrational coefficients yet roots 00 and 22, which are rational. Irrational roots occur in conjugate pairs only when the coefficients are rational, not the other way round.
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Original question written in the NDA 2023 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