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,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.

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.

If p , q , ra n ds are real numbers such that p r=2(q+s), then show that at least one of the equations x^2+p x+q=0 and x^2+r x+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.

If the roots of both the equations px^(2)+2qx+r=0 and qx^(2)-sqrt(pr)x+q=0 are real,then

If p, q, are real and p ne q then the roots of the equation (p-q) x^(2)+5(p+q) x-2(p-q)=0 are

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.