If p,q,r,s are real and `prgt4(q+s)` then show that at least one of the equations `x^2+px+q=0 and x^2+rx+s=0` has real roots.

Determine or proving the nature of the roots: If p;q;r;s are real no.such that pr=2(q+s) then show that atleast one of the equations x^(2)+px+q=0 and x^(2)+rx+s=0 has real roots.

Show that if p,q,r and s are real numbers and pr=2(q+s) , then atleast one of the equations x^(2)+px+q=0 and x^(2)=rx+s=0 has real roots.

If p,q,r and s are real numbers such that pr=2(q+s), then show that at least one of the equations x^(2)+px+q=0 and x^(2)+rx+s=0 has real roots.

If p,qr are real and p!=q, then show that the roots of the equation (p-q)x^(2)+5(p+q)x-2(p-q=0 are real and unequal.

If p, a,rare real and p!=q ,then show that the roots of the equation (p-q)x^(2)+5(p+q)x-2(p-q)=0 are real and unequal.

If p,q are real p!=q, then show that the roots of the equation (p-q)x^(2)+5(p+q)x-2(p-q)=0 are real and unequal.