24. A polynomial of degree 10 has three distinct roots. What is the maximum number of zero coefficients it can have?

(A. Khryabrov)
24. Answer: Answer: 9 zero coefficients. For example, the polynomial $x^{10}-x^{8}$ has roots $0,1,-1$. If a polynomial has only one non-zero coefficient, it is of the form $a x^{10}$, and therefore has exactly one root.