MathDB

24

Part of 1999 National Olympiad First Round

Problems(1)

Turkish NMO First Round - 1999 P-24 (Algebra)

Source:

7/3/2012
Polynomial f(x) f\left(x\right) satisfies \left(x \minus{} 1\right)f\left(x \plus{} 1\right) \minus{} \left(x \plus{} 2\right)f\left(x\right) \equal{} 0 for every x∈ℜ x\in \Re. If f\left(2\right) \equal{} 6, f\left({\tfrac{3}{2}} \right) \equal{} ?
<spanclass=′latex−bold′>(A)</span> −6<spanclass=′latex−bold′>(B)</span> 0<spanclass=′latex−bold′>(C)</span> 32<spanclass=′latex−bold′>(D)</span> 158<spanclass=′latex−bold′>(E)</span> None<span class='latex-bold'>(A)</span>\ -6 \qquad<span class='latex-bold'>(B)</span>\ 0 \qquad<span class='latex-bold'>(C)</span>\ \frac {3}{2} \qquad<span class='latex-bold'>(D)</span>\ \frac {15}{8} \qquad<span class='latex-bold'>(E)</span>\ \text{None}
algebrapolynomial