If the equations `x^2-x-p = 0` and `x^2 + 2px-12 = 0` have a common root, then that root is

If the equations px^2+2qx+r=0 and px^2+2rx+q=0 have a common root then p+q+4r=

If the equations px^2+2qx+r=0 and px^2+2rx+q=0 have a common root then p+q+4r=

If the equations x^(2) -px +q=0 and x^(2)+qx-p=0 have a common root, then which one of the following is correct?

If the equations x^(2)+ax+b=0 and x^(2)+a'x+b'=0 have a common root then this common root is equal to

If the equation x^2 + px + q =0 and x^2 + p' x + q' =0 have common roots, show that it must be equal to (pq' - p'q)/(q-q') or (q-q')/(p'-p) .