`ax^(2)+a=a^(2)x+x`

If 4x + 3a = 0 , then what is the value of (x^(2) + ax + a^(2))/(x^(3) - a^(3)) -(x^(2) -ax + a^(2))/(x^(3) + a^(3)) ?

For what values of a is the inequality (x^(2) +ax-2)/( x^(2) -x+1) lt 2 satisfied for all real values of x?

Two distinct polynomials f(x) and g(x) defined as defined as follow : f(x) =x^(2) +ax+2,g(x) =x^(2) +2x+a if the equations f(x) =0 and g(x) =0 have a common root then the sum of roots of the equation f(x) +g(x) =0 is -

If f(x)=x^(2)+ax-2a^(2)+1,g(x)=x-a,q(x)=x+2aandf(x)=g(x)*q(x)+r(x) then r(x) =

If f(x) = |(a, -1, 0), (ax, a,-1 ) ,(ax^(2), ax, a)| , then f(2x)-f(x) is divisible by 1) a 2) b 3) c ,d ,e 4). none of these