Question

If p is selected from the interval [0,5], then the probability that the equation 4x² + 4px + (p + 2) = 0 has real roots

(a)   1/2

(b)   1/4

(c)   3/5

(d)   2/5

Answer 1

Correct option  (c)  3/5

Explanation:

For real roots, D ≥ 0

⇒  p²– p – 2 ≥ 0

⇒  p ≤ –1 p ≥ 2

∴ p  ∈ [2,5] but p ∈ [0,5]

∴ required probability  = 5 -2/5 - 0 = 3/5