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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?


4 years ago

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

4 years ago
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