PrepRung
Sign inSign up free

NDA 2019 Maths · Mathematics · Quadratic Equations · easy

The inequality x^2+x+1>0 holds for every real x. 2. The equation x^2+2x+3=0 has two distinct real roots.

Single correct option

Consider the following statements:
1. The inequality x2+x+1>0x^2+x+1>0 holds for every real xx.
2. The equation x2+2x+3=0x^2+2x+3=0 has two distinct real roots.
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

For statement 1 the discriminant is 1−4=−3<01-4=-3<0 and the leading coefficient is positive, so the expression is always positive; it is true. For statement 2 the discriminant is 4−12=−8<04-12=-8<0, so the roots are non-real; it is false. Only statement 1 is correct. Checking the discriminant is the fastest way to settle both.
Report a mistake

Original question written in the NDA 2019 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