If `x^3+px+r` and `3x^2+p` have a common factor then value of `p^3/27+r^2/4=`

If x^(3)+px+r and 3x^(2)+p have common factor

If f(x)=x^(2)+5x+p and g(x)=x^(2)+3x+q have a common factor, then (p-q)^(2)=

Prove that if the equations x^2+px+r=0 and x^2+rx+p=0 have a common root then either p=r or , 1+p+r=0.

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)-3x+2=0,3x^(2)+px+q=0 have two roots common then the value of p and q is

If (x-3) is a factor of (x^2+4px-11p) then what is the value of 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^(3)+x^(2)-4x=4 and x^(2)+px+2p=0(p in R) have two roots common,then the value of p is

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)