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 :

Step-by-step solution

aligned & 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) aligned fav. cases =38 Prob. : 38 6 6 6