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The integral values of a for which the quadratic equation (x – a)(x – 10) + 1 = 0 has integral roots are
a. -1, 3
b. 2, 3
c. 12, 8
d. -8, -12
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3 Answers
341Suppose the quadratic has an integer root α, then we must have
(\alpha-10)(\alpha-a) = -1 where both factors are integers
i.e one of the factors is 1 is -1. Their difference is 2.
Hence |10-a| =2 \Rightarrow a=8,12
