consider the equation x^2+kx+1=0

Question

a single fair die(dice)is rolled to determine the value of the middle coefficient, k. the value for k is the number of dots on the upper face of the die. what is the probability that the equation will have real, unequal roots?

Answer 1

for the roots to be real and distinct, the discriminant must be positive.

k^2 - 4 > 0
k > 2

so, we need to roll a 3,4,5,6

p(k>2) = 4/6 = 2/3