If the coificients of the quadratic equations ax(squared)+bx+c=0is obtain by throwing a fair dice.find the probability that roots has real roots

dear student,

for real roots the condition is 

b^2 >= 4ac

for b=1 no chance

for b=2 only a=c=1 -> total = 1

for b=3 -> a,c either 1 or 2 but not 2 both -> total = 3

for b=4 -> total = 6

for b=5 -> toal = 12

for b=6 -> total = 17

=> probability = 1+3+6+12+17/6*6*6 = 13/108

i hope this explains !!