The value of x in given equation `px^2-q^2=0 ​`

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

If 2,3 are the roots of the equation 2x^3+px^2-13x+q=0 then (p,q) is

if the difference of the roots of the equation x^(2)-px +q=0 is unity.

If alpha,beta are roots of the equation x^(2)+px+q=0 ,then the equation whose roots are (q)/(alpha),(q)/(beta) will be

If difference of roots of the equation x^(2)-px+q=0 is 1, then p^(2)+4q^(2) equals-

If the abscissa and ordinates of two points P and Q are the roots of the equations x^(2)+2ax-b^(2)=0 and x^(2)+2px-q^(2)=0 respectively,then find the equation of the circle with PQ as diameter.

If the difference between the roots of the equation x^(2)-px+q=0 is the same as the difference of the roots of the equation x^(2)-qx+p=0 ,show that p+q+4=0 or p=q.

If the sum as well as the product of the roots of the equation px^2-6x + q=0 is 6, then what is (p + q) equal to?