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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2015 · Mathematics · Quadratic Equation

The number of real roots of the equation x^2-3|x|+2=0 is

The number of real roots of the equation x2−3∣x∣+2=0x^2-3|x|+2=0 is

Options

  1. A4
  2. B3
  3. C2
  4. D1

Correct answer

A. 4

Step-by-step solution

x2−3∣x∣+2=0\mathrm{x}^2-3|\mathrm{x}|+2=0 Case (i) when x≥0x \geq 0x2−3x+2=0(x−1)(x−2)=0\begin{aligned} & x^2-3 x+2=0 \\ & (x-1)(x-2)=0 \end{aligned}x=1,2x=1,2 (both roots satisfy the condition x≥0)x \geq 0) Case (ii) when x<0\mathrm{x} < 0x2+3x+2=0(x+1)(x+2)=0x=−1,−2( both roots satisfy the condition x<0)\begin{aligned} & x^2+3 x+2=0 \\ & (x+1)(x+2)=0 \\ & x=-1,-2(\text{ both roots satisfy the condition } x < 0) \end{aligned}$$ So no. of real roots is 4.
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