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Problems > High School Math > 2007

Polynomial Madness

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


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