Question ONE:

Let 'a' and 'b' be integers neither wof which is equal to zero. Prove that the equation...

a^2x^3 +b^2x^2– 1 = 0

...has no integer roots.

Question TWO:

For which real values of 'a' do the equations...

x^3 +ax+ 1 = 0 andx^4 +ax^2 + 1 = 0

...have a common root?