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NDA2017MathematicsQuadratic EquationActual

It is given that the roots of the equation x ^2-4 x - ₃ P =0 are real. For this, the minimum value of P is

Options

  1. A1 27
  2. B1 64
  3. C1 81
  4. D1

Correct answer

C. 1 81

Step-by-step solution

x ^2-4 x - ₃ P =0 We know, roots are real if discriminant is greater than or equal to 0 . i.e., b ^2-4 ac 0 ~b ^2 4 ac In the given equation, a=1, b=-4, c=- ₃ P . b ^2 4 ac (-4)^2 4(1) (- ₃ P ) aligned & b ^2 4 ac (-4)^2 4(1) (- ₃ P ) & 16 -4 ₃ P & 4 - ₃ P aligned 4 ₃ ( 1 P ) ( - a = 1 a ) 3^4 1 P 81 1 P P 1 81 . The minimum value of P is 1 81 .

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