The coefficients a , b , c in the quadratic equation a x 2 + b x + c = 0 are from the set { 1 , 2 , 3 , 4 , 5 , 6 } . If the probability of this equation having one real root bigger than the other is

Question

The coefficients a , b , c in the quadratic equation a x 2 + b x + c = 0 are from the set { 1 , 2 , 3 , 4 , 5 , 6 } . If the probability of this equation having one real root bigger than the other is p , then 216 p equals :

TestHub · Accepted Answer

​ D > 0 b 2 > 4 ac b = 3 : ( a , c ) = ( 1 , 1 ) ( 1 , 2 ) ( 2 , 1 ) b = 4 : ( a , c ) = ( 1 , 1 ) ( 1 , 2 ) ( 2 , 1 ) ( 1 , 3 ) ( 3 , 1 ) b = 5 : ( a , c ) = ( 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 ) b = 6 : ( a , c ) = ( 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 , 4 ) ( 4 , 2 ) ( 2 , 2 ) ​ fav. cases = 38 Prob. : 6 × 6 × 6 38 ​

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