Aman verma wrote:Q: Each coefficient in the equation ax^2 + bx + c = 0 is determined by throwing ordinary six faced die . Find the probability that the equation will have real roots
a) 34/161
b)43/216
c)25/161
d) 47/216
e)31/216
An equation ax^2 + bx + c = 0 has real roots when b^2 is greater than 4*a*c
There are 6*6*6 ways to choose coefficients
when b=1 there is no roots no matter what
when b=2 there are roots only when a=1 and c=1 - 1 way
when b =3 (1,1), (2,1) and (1,2) satisfies condition - 3 ways
when b= 4 (1,1), (1,2) (2,1) (2,2) (1,3) (3,1) (1,4) (4,1) satisfies the conditon - 8 ways
when b=5 (1,1),(1,2), (2,1), (1,3), (3,1), (1,4), (4,1), (1,5),(5,1) (1,6) (6,1), (2,3), (3,2), (2,2) - 14 ways
when b=6 (1,1),(1,2), (2,1), (1,3), (3,1), (1,4), (4,1), (1,5),(5,1) (1,6) (6,1), (2,3), (3,2), (2,2) (2,4), (4,2),(3,3) - 17 ways
total of 43 ways
Probability = 43/216
Always borrow money from a pessimist, he doesn't expect to be paid back.
