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…

MHT CET 2026 Mathematics question

Let be an integer selected at random from the set . The probability that the equation has real roots is…

(A)Correct
(B)
(C)
(D)

Answer: (A)

Solution

The set has equally likely integers. For the equation reduces to , which has no roots, so is not favourable. For it is a genuine quadratic with real roots iff the discriminant , i.e. ; for positive this means . So , which is

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Question ID VK-101058