If pϵW is chosen at random from the interval [0,6], then the probability that the roots of the equation x2+px+14(p+2)=0 will be real is
A
35
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B
12
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C
34
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D
57
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Solution
The correct option is D57 Discriminant of given quadratic is D=p2−p−2=(P+1)(P−2) For roots to be real D≥0⇒P≤−1,P≥2 Hence n(E)=n{2,3,4,5,6}=5,n(S)=n{0,1,2,3,4,5,6}=7 Hence required probability =n(E)n(S)=57