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MHT CET202619 April 2026Morning ShiftMathematicsQuadratic EquationActual

Let a be an integer selected at random from the set 0, 1, 2, 3, , 9 . The probability that the equation ax^2 - ax + 1 = 0 has real roots is ...

Options

  1. A3 5
  2. B1 2
  3. C2 5
  4. D5 9

Correct answer

A. 3 5

Step-by-step solution

The total number of possible values for a from the set 0, 1, 2, 3, , 9 is 10 . For the equation ax^2 - ax + 1 = 0 to have real roots, we consider two cases: If a = 0 , the equation becomes 1 = 0 , which has no roots. If a 0 , the equation is a quadratic equation. For it to have real roots, its discriminant must be non-negative. D = (-a)^2 - 4(a)(1) 0 a^2 - 4a 0 a(a - 4) 0 Since a 1, 2, 3, , 9 , the condition a(a - 4) 0 is satisfied when a 4 . The favorable values of a are 4, 5, 6, 7, 8, 9 . The number of favorable

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