Question

The values of $a$ for which the sum of roots of the equation $x^2+(2-a-a^2)x-a^2=0$ is zero are $\alpha$ and $\beta$ then $|\alpha +\beta |=$

Answer 1

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

sum of goals $=-\frac{(2-a-a^2)}{1}=0$

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

$\Rightarrow a^2+2a-a-2=0$ k

$\Rightarrow a(a+2)-1(a+2)=0$

$\Rightarrow (a-1)(a+2)=0$

$\Rightarrow a=1,-2$

$\Rightarrow \alpha =1,\beta =-2$

$|\alpha +\beta |=|1-2|=|-1|=1$