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NDA 2018 Maths · Mathematics · Quadratic Equations · easy

If a>0 and b^2-4ac<0, then ax^2+bx+c>0 for every real x. 2. The equation x^2-x+1=0 has two distinct real roots.

Single correct option

Consider the following statements: 1. If a>0a>0 and b2−4ac<0b^2-4ac<0, then ax2+bx+c>0ax^2+bx+c>0 for every real xx. 2. The equation x2−x+1=0x^2-x+1=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 a>0a>0 and negative discriminant the parabola opens upward and never meets the x-axis, so the expression is always positive: statement 1 is true. For x2−x+1x^2-x+1 the discriminant is 1−4=−3<01-4=-3<0, so the roots are complex: statement 2 is false.
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Original question written in the NDA 2018 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