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AP EAMCET201823 Apr 2018Morning ShiftMathematicsQuadratic EquationActual

Let a, b and c be three positive real numbers such that the sum of any two of them is greater than the third. All the values of such that the roots of the equation x^2+2(a+b+c) x+3 (a b+b c+c a)=0 are real, are given by

Options

  1. A< 2 3
  2. B2 3
  3. C< 4 3
  4. D1 3 < < 2 3

Correct answer

C. < 4 3

Step-by-step solution

Roots of the equation x^2+2(a+b+c) x+3 (a b+b c+c a)=0 are real, so aligned & [2(a+b+c)]^2-4(1)[3 (a b+b c+c a)] 0 & a^2+b^2+c^2+2(a b+b c+c a) 3(a b+b c+c a) aligned Now, sum of two roots is greater than thirds So, aligned & a Adding Eqs. (ii), (iii) and (iv), we get aligned & a^2+b^2+c^2 < 2 3 + 2 3 < 4 3

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