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For what integral values of 'a' the equation x^2-x(1-a)-(a+2)=0 has integral roots?

For what integral values of 'a' the equation x^2-x(1-a)-(a+2)=0 has integral roots?

Grade:12

1 Answers

jagdish singh singh
173 Points
7 years ago
\hspace{-0.7 cm}$Given $x^2-x(1-a)-(a+2) = 0$ as $(x-1)(x+a) = 2\; \forall x,a\in \mathbb{Z}$\\\\ So $(x-1)(x+a) = 2\times 1 = 1\times 2 = -2\times -1=-1\times -2$\\\\ $\bullet \; (x-1)(x+a) = 2\times 1 \;,$ Then $x-1=2\cap x+a=1,$ So $a=-2\\\\ \bullet \; (x-1)(x+a) = 1\times 2\;,$ Then $x-1=1\cap x+a=2,$ So $a=0\\\\ \bullet \; (x-1)(x+a) = -2\times -1\;,$ Then $x-1=-2\cap x+a=-1,a=0\\\\ \bullet \; (x-1)(x+a) = -1\times -2\;,$ Then $x-1=-1\cap x+a=-2,a=-2 \\\\

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