The coefficients of a quadratic equation ax2+bx+c=0(a≠b≠c) are chosen from first three prime numbers, the probability that roots ofthe equation are real is

The coefficients of a quadratic equation ax2+bx+c=0(abc) are chosen from first three prime numbers, the probability that roots of
the equation are real is

  1. A

  2. B

  3. C

    ¼

  4. D

    ¾

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    Solution:

     First three prime numbers are 2, 3 and 5
    Total ways of choosing a, b, c = 3 x 2 x 1= 6   [abc]
    For roots to be real ,b24ac0

    Value of b              Possible values of a and c

    2                             44ac0ac1a=c=1

                                    (No values of a and c)

    3                             94ac0ac94ac=1,ac=2a=c=1,a=2,c=1a=1,c=2

                                    (No values of a and c)

    5                            254ac0ac254ac=1,2,3,4,5,6ac1,2,3,4,5 for ac=6(2,3)(3,2)

    Favorable ways = 2

    Required probability = Favourable ways  Total ways 

                                     =26=13

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