A polynomial function fx has zeros at 1 i and 2 3i What ar

A polynomial function f(x) has zeros at 1 + i and 2 - 3i. What are some things that you know about the graph of f(x) and the equation of f(x)? Try and come up with at least three things for both the graph and the equation. A polynomial function f(x) has zeros at 1 + i and 2 - 3i. Is the graph of the function below a possible sketch of f(x)? Explain.

Solution

1) x= 1+ i ; x = 2- 3i

---- f(x) also has another set of roots i.e. x= 1-i ; x= 2+3i which are complex conjugate of the roots given

------f(x) is atleast a 4rth degree polynomial

----- It is a polynomial with Domain ( - inf , inf)

Graph of f(x):

--- If it has only two complex conjugate set of roots,then

there are no real roots and graph does not cut the x axis.

--- If it is an even degree polynomial then both ends of graph have end in same

direction.

2) The graph given in figuere can be the graph of polynomial f(x)

as both ends of the graph end upwars in same direction.

It is possibel that f(x) is even function we have roots : x = 1-i , 1+i ; x= 2+3i , 2-3i

further graph has two roots : x= -2 ; x= 5.In total six roots and 6 degree polynomial.