Probability Practice Test 2

Question : 6 of 37

Marks: +1, -0

If an integer p is chosen at random in the interval 0 ≤ p ≤ 5, the probability that the roots of the equation

x^2 + px + p/4 + 1/2 = 0

are real is

Solution:

Roots of the equation

x^2 + px + p/4 + 1/2 = 0

are real if

\Δ = p^2 - 4 (p/4 + 1/2) ≥ 0

i.e., (p – 2) (p + 1)  0 i.e., p ≤ –1 or p ≥ 2
In 0 ≤ p ≤ 5, possible values of p are 2, 3, 4, 5
Thus, probability

= 4/6 = 2/3

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