basic algebra

[vaibhav101]

if a,b are the roots of $$x^2+px+q=0$$ , and g,d are the roots of $$x^2+px-r=0$$ , then (a-g)(a-d) is equal to
A q+r
B q-r
C -q-r
D -2(p+q+r)
E r-q

[deloitte247]

$$x^2+px+q=0\ \left(have\ roots\ a,b\right)$$
$$a+6=-p$$
$$ab=q$$
$$a^2+pa+q=0$$
$$x^2+px-r=0\ \left(have\ roots\ g,d\right)$$
$$g+d=-p$$
$$gd=-r$$
$$\left(a-g\right)\left(a-d\right)=a^2-\left(g-d\right)a+gd$$
$$=-q-r$$
$$Option\ C\ is\ the\ answer$$