Show that the roots of the equation `x^2 + px - q^2 = 0` are real for all real values of p and q.

If p and q are the roots of the equation x^2+px+q =0, then

If p and q are the roots of the quadratic equation x^(2)+px-q=0 , then find the values of p and q.

If 2+ i sqrt3 is a root of the equation x^(2)+px+q=0 , where p and q are real then find the value of p and q.

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.