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Find all the integers a such that (x-a)(x-12)+2 can be factored as (x+b)(x+c) where b and c are integers.
Asked by vikasg13.hardware | 07 Aug, 2018, 05:40: PM
(x - a)(x - 12) + 2
= x2 - 12x - ax + 12a + 2
= x2 - (12 + a)x + 12a + 2
Discriminant D = a2 - 24a + 136
If a = 9 then x = 10 or 11
If a = 15 then x = 13 or 14
a = 9 will give you x2 - 21x + 110 = (x - 10)(x - 11)
a = 15 will give you x2 - 27x + 182 = (x - 13)(x - 14)
Answered by Sneha shidid | 08 Aug, 2018, 10:32: AM

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