The coefficients a, b, c in the quadratic equation a x^2+b x+c=0 are chosen from the set 1,2,3,4,5,6,7,8 . The probability of this equation having repeated roots is :

Step-by-step solution

aligned & a x^2+b x+c=0 & a, b, c 1,2,3,4,5,6,7,8 & Repeated roots D=0 & b^2-4 a c=0 b^2=4 a c & Prob = 8 8 8 8 = 1 64 & (a, b, c) & (1,2,1) ;(2,4,2) ;(1,4,4) ;(4,4,1) ;(3,6,3) ; & (2,8,8) ;(8,8,2) ;(4,8,4) & 8 case aligned