Q153 / 270 · NDA 2016 (Phase 1) · Mathematics

If $x^2+p x+4 \gt 0$ for all real values of $x$, then which one of the following is correct?

  • A
    $|\mathrm{p}| \lt 4$
  • Correct answer
    B
    $|\mathrm{p}| \leq 4$
  • C
    $|\mathrm{p}| \gt 4$
  • D
    $|\mathrm{p}| \geq 4$

Solution

$x^2-p x+4 \gt 0 \quad \forall$ real values of $x$ $\begin{aligned} & \text { If } b^2-4 a c \leq 0 \\ & \Rightarrow p^2-4(1)(4) \leq 0 \\ & \Rightarrow p^2 \leq 16 \Rightarrow|p| \leq 4 \end{aligned}$

Hence, the correct answer is option: 'B'.

Relevant Questions