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Manipal MET2020MathematicsQuadratic Equation

The sum of the real solutions of equation 2|x|^2+51=|1+20 x| is

Options

  1. A5
  2. B24
  3. C0
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

Given, 2|x|^2+51=|1+20 x| Then, following two possible cases aris 9 : Casel When 1+20 x 0 array lr & x - 1 20 & 2 x^2+51=(1+20 x) & 2 x^2-20 x+50=0 array x^2-10 x+25=0 [ 2 0] (x-5)^2=0 x=5,5 Case II When 1+20 x 0 array lc & x - 1 20 & 2 x^2+51=-(1+20 x) & 2 x^2-20 x+52=0 & x^2-10 x+26=0 array Here, D 0 Thus, roots are-imaginary. Hence, sum of real roots =5+5=10

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