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AP EAMCET201824 Apr 2018Morning ShiftMathematicsQuadratic EquationActual

If the quadratic equation 4^ ^2 x^2+2 x+ ( ^2- + 1 2 )=0 has real roots, then the value of ^2 + ⁻¹ is

Options

  1. A3
  2. B3 +1
  3. C2
  4. D2 -1

Correct answer

B. 3 +1

Step-by-step solution

The quadratic equation, aligned & 4^ ^2 x^2+2 x+ ( ^2- + 1 2 )=0 have real roots & discriminant =4-4 4^ ^2 ( ^2- + 1 2 ) 0 & 4^ ^2 ( ^2- + 1 2 ) 1 & But 4^ ^2 4, ^2- + 1 2 = ( - 1 2 )^2+ 1 4 1 4 aligned So, the equation will be satisfied only aligned & When 4^ ^2 =4 and ^2- + 1 2 = 1 4 & ^2 =1 and ( - 1 2 )^2=0 & ^2 =1 and = 1 2 & ^2 + ⁻¹ =1+ ⁻¹(1 / 2) & =1+ / 3 aligned

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