Question 136
We say a polynomial of degree three with integer coefficients is *good* if it has three real roots and all its roots are irrational numbers between $0$ and $1$.
(i) Is there a good polynomial with leading coefficient equal to $10$?
(ii) Is there a good polynomial with leading coefficient equal to $13$?
(i) Is there a good polynomial with leading coefficient equal to $10$?
(ii) Is there a good polynomial with leading coefficient equal to $13$?