[" The common roots of the equations "],[x^(3)+2x^(2)+2x+1=0" and "1+x^(200)+x^(2023)],[" are ( "omega" is non real cube root of unity) "]

The common roots of the equation x^(3) + 2x^(2) + 2x + 1 = 0 and 1+ x^(2008)+ x^(2003) = 0 are (where omega is a complex cube root of unity)

The common roots of the equation x^(3) + 2x^(2) + 2x + 1 = 0 and 1+ x^(2008)+ x^(2003) = 0 are (where omega is a complex cube root of unity)

The number of real roots of the equation x^(4)+x^(3)+2x^(2)+x+1=0 is

If x=1 is a common root of the equations a x^2+a x+3=0 and x^2+x+b=0 , then a b=

The number of real roots of the equation 1+3^(x//2)=2^(x) , is

The number of real roots of the equation 1+3^(x//2)=2^(x) , is

If the equations x^(2) + 2x -3=0 and x^(2) + 3x-m=0 have a common root, then the non- zero value of m.

The equations x^(2)-2x+1=0,x^(2)-3x+2=0 have a common root then that common root is

alpha,beta and gamma are the roots of x^(3)-3x^(2)+3x+7=0 then sum((alpha-1)/(beta-1)) is (where omega is a cube root of unity)