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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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