If α,β be the roots of x2+px+q=0 and α+h,β+h are the roots of x2+rx+s=0, then

α+β=-p, αβ=qα+β+2h=-r, (α+h)(β+h)=s-p+2h=-r⇒h=p-r2   ...(i)Now, αβ+h(α+β)+h2=s⇒q+h(-p)+h2=s⇒q+(p-r2)(-p)+p-r22=s⇒q-(p2-pr)2+p2+r2-2pr4=s⇒4q-2p2+2pr+p2+r2-2pr=4s⇒4q-p2+r2-4s=0⇒r2-4s=p2-4q.