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If and only if
p*q = c
p+q = b
For
p*q = -35
p+q = -2
Look at factors of -35:
-35 and 1 --> -35 + 1 = -34, NO
35 and -1 --> 35 - 1 = 34, NO
-7 and 5 --> -7 + 5 = -2, YES
7 and -5 --> 7 -5 = 2, NO
thus p = -7, q = 5
