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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2013 · Mathematics · Quadratic Equation

How many real roots does the quadratic equation f(x)=x^2+3|x|+2=0...

How many real roots does the quadratic equation f(x)=x2+3∣x∣+2=0f(x)=x^2+3|x|+2=0 have?

Options

  1. AOne
  2. BTwo
  3. CFour
  4. DNo real root

Correct answer

D. No real root

Step-by-step solution

Case-1, when x>0,∣x∣=xx > 0,|x|=xf(x)=x2+3x+2=0(x+2)(x+1)=0x=−1 and −2\begin{aligned} f(x)=x^2+3 x+2 & =0 \\ (x+2)(x+1) & =0 \quad x=-1 \text{ and }-2 \end{aligned}But $x > 0$, Hence, no roots exist. Case-II, when $x < 0,|x|=-x\begin{aligned} f(x)=x^2-3 x+2 & =0 \\ (x-2)(x-1) & =0 x=+1,2 \end{aligned}$$ButButx < 0$, Hence, no real roots exist again.
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