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Black Book Advanced Problems in MathematicsMathematicsQuadratic Equation

For the quadratic polynomial f(x) = 4x^2 - 8ax + a , the statements(s) which hold good is/are :

Options

  1. AThere is only one integral ' a ' for which f(x) is non-negative x R
  2. BFor a < 0 , the number zero lies between the zeroes of the polynomial
  3. Cf(x) = 0 has two distinct solutions in (0, 1) for a ( 1 4 , 4 7 )
  4. DThe minimum value of f(x) for minimum value of a for which f(x) is non-negative x R is 0 .

Correct answer

A. There is only one integral ' a ' for which f(x) is non-negative x R

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