Question

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

Answer 1

Solution :-

Given equation $x^2-x(1-a)-(a+2)=0$

It will have integral roots when $b^2-4ac=0$

$\Rightarrow (1-a{)}^2-4(1\left)\right(-1(a+2))=0$

$\Rightarrow a^2+2a+9=0$

Now completing the square or by quadratic formula

$a=\frac{-2\pm \sqrt{4-36}}{2}=\frac{-2\pm \sqrt{-32}}{2}=-1\pm 2\sqrt{2}$

There will not be an integral value.