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Question

If m is selected at random from set {1,2,10} and the probability that the quadratic equation 2x2+2mx+m+1=0 has real root is k then value of 5k is ?

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Solution

2x2+2mx+m+1=0 has real roots
4m24.2.(m+1)
4m28m80
m22m20
[m(1m)][m(1+3)]0
m(13) Or m(13)
m0.73 Or m2.7
m=3,4,5,6,7,8,9,10
Probability k=8C110C1=810=45
5k=4

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