1. The zeros of the polynomial
x3 - 33x2 + 354x + k
are in arithmetic progression. What is the value of k?
2. Let f(x) = px5+qx4+rx3+sx2+tx+1 be a polynomial such that f(1)=4, f(2)=11 and all the
coefficients p,q,r,s and t are integers. Prove that the equation f(x)=0 has no
integer roots.
Source: unknown
| 