The given equation is $bc{x}^2+2\left(b+c-a\right)x+a=0$ 

$\mathrm{\Delta }=4(\mathrm{b}+\mathrm{c}-\mathrm{a}{)}^2-4\mathrm{abc}=4\left((\mathrm{b}+\mathrm{c}-\mathrm{a}{)}^2-\mathrm{abc}\right)>0$
$\text{product of roots }=\frac{\mathrm{a}}{\mathrm{bc}}=\frac{{\mathrm{a}}^2}{\mathrm{abc}}<0$
One root is +ve and other root is negative.