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Q.

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 roots, is

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a

18

b

19

c

45

d

12

answer is C.

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Detailed Solution

2x2+2mx+m+1=0 For real roots, D≥0⇒4m2−8(m+1)≥0m2−2m−2≥0∴(m−1)2≥3⇒m≥1+3=2.7⇒m=3,4,5,6,7,8,9,10 are favourable cases P(A)=810
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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 roots, is