If equations `x^3 + 3px^2 + 3qx + r = 0 and x^2 + 2px + q = 0` have a common root, show that `4 (p^2 — q) (q^2 – pr) = (pq – r)^2`

If equations x^(3)+3px^(2)+3qx+r=0 and x^(2)+2px+q=0 have a common root,show that 4(p^(2)q)(q^(2)pr)=(pqr)^(2)

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) .

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, which of the following can be true?

If the equations px^(2)+qx+r=0 and rx^(2)+qx+p=0 have a negative common root then the value of (p-q+r)=

IF x^2 +px + q=0 and x^2 + qx +p=0 have a common root , then their other roots are the roots of

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

Show that the equations px^2+qx+r=0 and qx^2+px+r=0 will have a common root if p+q+r=0 or, p=q=r.