PrepRung
Sign inSign up free

NDA 2021 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 real coefficients and negative discriminant has two conjugate complex…

Single correct option

Which of the statements is/are correct? 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 real coefficients and negative discriminant has two conjugate complex roots.
  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

Statement 1: substituting x=1x=1 gives a+b+c=0a+b+c=0, which holds. Statement 2: for real coefficients the non-real roots arise as −b±i∣D∣2a\dfrac{-b\pm i\sqrt{|D|}}{2a}, a conjugate pair. Both are correct.
Report a mistake

Original question written in the NDA 2021 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