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How many real roots does the quadratic equation f(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|=x aligned f(x)=x^2+3 x+2 & =0 (x+2)(x+1) & =0 x=-1 and -2 aligned But x 0 , Hence, no roots exist. Case-II, when x 0,|x|=-x aligned f(x)=x^2-3 x+2 & =0 (x-2)(x-1) & =0 x=+1,2 aligned But x 0 , Hence, no real roots exist again.

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