The product of the two roots of is an integer. Find its units digit.
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Let 2 0 1 4 x = a . We get 2 0 1 4 a 2 + 0 . 5 = 2 0 1 4 2 0 1 4 So a 2 − 2 0 1 4 a + 0 . 5 = 0 If x 1 , x 2 were the solutions to the original equation and a 1 , a 2 for the second equation, x 1 × x 2 = 2 0 1 4 a 1 + a 1 = 2 0 1 4 2 0 1 4 The units digit of powers of 4 varies as 4 , 6 , 4 , 6 . . . and 2014 is even so the answer is 6