ProbabilityHard
Question
If an integer q is chosen at random in the interval - 10 ≤ q ≤ 10, then the probability that the roots of the equation x2 + qx + 
+ 1 = 0 are real is
+ 1 = 0 are real is Options
A.16/21
B.15/21
C.14/21
D.17/21
Solution
Roots of the equation x2 + qx +
+ 1 = 0 are real if
ᐃ = q2 - 4
≥ 0
⇒ q2 - 3q - 4 ≥ 0
⇒ (q + 1) (q - 4) ≥ 0
⇒ q ≤ - 1 or q ≥ 4.
⇒ possible value of q are 4, 5, 6, 7, 8, 9, 10, - 10, - 9, - 8, - 7, - 6, - 5, - 4, - 3, - 2, - 1.
⇒ probability =
+ 1 = 0 are real ifᐃ = q2 - 4
≥ 0⇒ q2 - 3q - 4 ≥ 0
⇒ (q + 1) (q - 4) ≥ 0
⇒ q ≤ - 1 or q ≥ 4.
⇒ possible value of q are 4, 5, 6, 7, 8, 9, 10, - 10, - 9, - 8, - 7, - 6, - 5, - 4, - 3, - 2, - 1.
⇒ probability =
Create a free account to view solution
View Solution FreeMore Probability Questions
A cube is thrown 6 times, then probability of getting the digits 2 and 4 exactly three times each is-...A determinant is chosen at random from the set of all determinant of order 2 with elements 0 or 1 only. The probability ...In a series of 3 independent trials the probability of exactly 2 success is 12 times as large as the probability of 3 su...'A' writes a letter to his friend 'B' and does not receive a reply. It is known that one out of ' $n$ ' letters does not...One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional...