The equation `x^3+px^2+qx+r=0 and x^3+p\'x^2+q\'x+r'=0` have two common roots, find the quadratic whose roots are these two common roots.

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

If every pair from among the equations x^2+px+qr=0,x^2+qx+rp=0 and x^2+rx+pq=0 has a common root, then the sum of the three common roots is

If every pair from among the equations x^2 + px + qr = 0, x^2 + qx +rp = 0 and x^2+rx +pq = 0 has a common root then the product of three common root is

IF the equations x^(3) + 5x^(2) + px + q = 0 and x^(3) + 7x^(2) + px + r = 0 have two roots in common, then the product of two non-common roots of two equations, is

If x^(2)-6x+5=0 and x^(2)-3ax+35=0 have common root, then find a.

If the equations ax^2 + bx + c = 0 and x^3 + x - 2 = 0 have two common roots then show that 2a = 2b = c .

If the quadratic equations x^(2) +pqx +r=0 and z^(2) +prx +q=0 have a common root then the equation containing their other roots is/are

If two equations x^(2) + ax + bc = 0 and x^(2) + bx + ca =0 have a common root, the find the condition and the quadratic with other roots of the equations.

Find the equation whose roots are the cubes of the roots x^3 +3x^2 +2=0

If the equation x^(2) - 3x + b = 0 and x^(3) - 4x^(2) + qx = 0 , where b ne 0, q ne 0 have one common root and the second equation has two equal roots, then find the value of (q + b) .