If the equations `x^2 + abx + c=0` and `x^2 + acx + b = 0` have a common root, then their other roots satisfy the equation

If the equations x^(2) + ax + bc = 0 and x^(2) + bx + ca = 0 have a common root, then their other roots satisfy the equation

If the equations x^(2) - ax + b = 0 and x^(2) + bx - a = 0 have a common root, then

Prove that , if the equations x^2+bx+ca=0 and x^2+cx+ab=0 have only non-zero common root then their other roots satisfy the equation t^2+at+bc=0 .

If x^2 + bx + ca =0 , x^2 + cx +ab =0 have a common root then their other are the roots of the equation

If the equation x^(2)+ax+b=0 and x^(2)+bx+a=0 have a common root, then their other roots satisfy the equation

If the equation ax^(2) + bx + c = 0 and 2x^(2) + 3x + 4 = 0 have a common root, then a : b : c

If the equation ax^(2) + bx + c = 0 and 2x^(2) + 3x + 4 = 0 have a common root, then a : b : c