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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
13
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B
23
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C
35
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D
15
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Solution

The correct option is C 35
Discriminant D of the quadratic equation
x2+mx+12+m2=0 is given by
D=m24(12+m2)
=m22m2
=(m1)23
Now, as the roots of quadratic equation are real
D0(m1)23
This is possible for m=3,4 and 5.
Also, the total number of ways of choosing m is 5.
The probability of the required event =35.

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