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NDA 2020 Maths · Mathematics · Quadratic Equations · easy

The equation x^2+kx+4=0 has no real roots if and only if

Single correct option

The equation x2+kx+4=0x^2+kx+4=0 has no real roots if and only if
  1. A. k<−4k<-4 or k>4k>4
  2. B. k≥4k\ge4
  3. C. −2<k<2-2<k<2
  4. D. −4<k<4-4<k<4
Show answer and solution

Answer: (D) −4<k<4-4<k<4

No real roots needs discriminant k2−16<0k^2-16<0, i.e. k2<16k^2<16, so −4<k<4-4<k<4. The option k<−4k<-4 or k>4k>4 gives two distinct real roots instead, and the endpoints k=±4k=\pm4 give equal real roots, so they are excluded.
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Original question written in the NDA 2020 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