If quadratic equations `x^(2)+px+q=0` & `2x^(2)-4x+5=0` have a common root then` p+q` is never less than `{p,q in R}:-`

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

Suppose that the quadratic equations 3x^(2)+px+1=0 and 2x^(2)+qx+1=0 have a common root then the value of 5pq-2p^(2)-3q^(2)=

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+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 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)

Prove that equations (q-r)x^(2)+(r-p)x+p-q=0 and (r-p)x^(2)+(p-q)x+q-r=0 have a common root.

If the quadratic equation x^(2)-2x-m=0 and p(q-r)x^(2)-q(r-p)x+r(p-q)=0 have common root such that second equation has equal roots. Then the value of m is