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 :

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​ 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 ​ = 64 1 ​ ⇒ ( 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 ​

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