2016/114) Each coefficient of an equation $ax^2+bx+c=0$ is determined by throwing an ordinary die. find the probability that the equation shall have equal roots.

dice has to be thrown 3 times so number of ways = $6^3= 216$
for the equation to have equal roots we should have $b^2=4ac$
so b has to be even.
taking b=2 we have ac= 1 so a= 1, c = 1 one way
b=4 we have ac = 4 that in 3 ways (a = 1 , c= 4), ( a=2, c= 2), (a =4, c= 1)
b= 6 we have ac =9 in one way a=c=3
so number of ways = 5
hence probability is $\frac{5}{216}$