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 =
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