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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2016 · Mathematics · Quadratic Equation

If x^2+p x+4 > 0 for all real values of x , then which one of the...

If x2+px+4>0x^2+p x+4 > 0 for all real values of xx, then which one of the following is correct?

Options

  1. A∣p∣<4|\mathrm{p}| < 4
  2. B∣p∣≤4|\mathrm{p}| \leq 4
  3. C∣p∣>4|\mathrm{p}| > 4
  4. D∣p∣≥4|\mathrm{p}| \geq 4

Correct answer

B. ∣p∣≤4|\mathrm{p}| \leq 4

Step-by-step solution

x2−px+4>0∀x^2-p x+4 > 0 \quad \forall real values of xx If b2−4ac≤0⇒p2−4(1)(4)≤0⇒p2≤16⇒∣p∣≤4\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}$$
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