Question

find the polynomial function f (x) with real coefficients having the given degree and zeros answer will vary depending on the choice of the leading coefficient.

Degree 4 ; zeros 3 + 2i , 4,multiplicity 2

 

Answer 1

Step 1 :

The degree of is , the zeros are , and the multiplicity is .

Since the degree of the polynomial is , the zeros of are .

From the conjugate pair theorem, complex zeros occur in conjugate pairs.

Conjugate of is .

Since the multiplicity is , the remaining zero is .

The four zeros are .

Step 2 :

If are the zeros of the polynomial , then the polynomial function can be written as , where is the leading coefficient of the polynomial.

Consider the leading coefficient as .

Hence, the polynomial function is and .

Solution :

The polynomial function is and .