Question

Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.)

2/3, -1, 3 + √2 i

Answer 1

Step 1:

Complex zero of polynomial  function and real zeros are .

Using complex conjugate root theorem is a zero of the polynomial function.

Required polynomial is fourth degree polynomial.

Step 2:

Zeros are and .

By using Factor theorem,

When then is factor of polynomial.

 

.

Solution:

The polynomial function .