Each coefficient in the equation ax2+bx+c=0 is determined by throwing an ordinary die. Find the probability that the equation will have equal roots.
The correct option is B 5216
Roots equal ⇒b2−4ac=0
(b2)2=ac
Each coefficient is an integer, so we consider the following cases:
If b=1
∴14=ac. No integral values of a and c.
If b=2
1=ac∴(1,1)
If b=3
92=ac No integral values of a and c.
If b=4
4=ac∴(1,4),(2,2),(4,1),
If b=5
252=ac, No integral values of a and c.
b=6
9=ac∴(3,3)
Thus we have 5 favourable ways for b=2,4,6
Total number of equations is 6×6×6=216 as each variable has 6 possible results, when a die is thrown.
∴ Required probability is 5216