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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2019 · Mathematics · Quadratic Equation

How many real roots does the equation x^3+3|x|+2=0 have?

How many real roots does the equation x3+3∣x∣+2=0x^3+3|x|+2=0 have?

Options

  1. AZero
  2. BOne
  3. CTwo
  4. DFour

Correct answer

A. Zero

Step-by-step solution

x2+3∣x∣+2=0=(∣x∣)2+3∣x∣+2=0⇒(∣x∣+1)(∣x∣+2)=0⇒∣x∣=−1,−2∴ No real roots exist. \begin{aligned} & x^2+3|x|+2=0 \\ & =(|x|)^2+3|x|+2=0 \\ & \Rightarrow(|x|+1)(|x|+2)=0 \\ & \Rightarrow|x|=-1,-2 \\ & \therefore \text{ No real roots exist. }\end{aligned}
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