If the numbers appeared on the two throws of a fair six faced die are α and β , then the probability that x 2 + α x + β > 0 , for all x ∈ R , is

Step-by-step solution

Total sample space of two dice will be equal to 6 × 6 = 36 Now for x 2 + α x + β > 0 its discriminant D must be less than zero, So D = b 2 - 4 a c < 0 or α 2 - 4 β < 0 ⇒ α 2 < 4 β Now, if α = 1 , β can take values 1 , 2 , 3 , 4 , 5 , 6 If α = 2 , β can take values 2 , 3 , 4 , 5 , 6 If α = 3 , β can take values 3 , 4 , 5 , 6 If α = 4 , β can take values 5 , 6 If α = 5 and 6 , no value of β possible So number of