Problem
Find the polynomial function \( f \) with real coefficients that has the given degree, zeros, and solution point. \( \begin{array}{ccc}\text { Degree } & \text { Zeros } & \text { Solution Point } \\ 4 & -1,2, \sqrt{2} i & f(1)=48\end{array} \)
Solution
Step 1 ：\(f(x)=a(x+1)(x-2)(x^2+2)\)
Step 2 ：\(48=a(1+1)(1-2)(1^2+2)\)
Step 3 ：\(a=48\)
