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Question

If m is a natural such that m5, then the probability that the quadratic equation x2+mx+12+m2=0 has real roots is


A

1/5

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B

2/3

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C

3/5

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D

1

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Solution

The correct option is C

3/5


Discriminant D of the quadratic equation
x2+mx+12+m2=0
is given by
D=m24(12+m2)=m22m2=(m1)23Now, D0(m1)23
This is possible for m=3, 4 and 5. Also, the total number of ways of choosing m is 5.
Probability of the required event= 3/5.


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