Find the fourthdegree polynomial function f with real coeffi

Find the fourth-degree polynomial function f with real coefficients that has the zeros x = plusminus Squareroot 2i and the x intercepts shown in the graph. f(x) = Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.) 4, -2t f(x) =

Solution

1) P(x) = (x - sqrt(2)i)(x + sqrt(2)i)(x + 3)(x - 2) = 0

=> (x² + 2)(x² + x - 6) = 0

=> x⁴ + x³ - 4x² + 2x - 12 = 0

f(x) = x⁴ + x³ - 4x² + 2x - 12

2) f(x) = (x - 4)(x + 2i)(x - 2i)

= (x -4)(x² + 4) = x³ - 4x² + 4x - 16