3. Non-zero integers $a, b, c$ are three consecutive terms of an increasing arithmetic progression. All six quadratic equations, whose coefficients are the numbers $a, b, 2c$, taken in any order, have two distinct roots. Find the smallest possible value of the common difference of the progression and the corresponding numbers $a, b, c$.
Answer: $d_{\min }=4 ; a=-5, b=-1, c=3$.