Question

Find a polynomial f(x) of degree 4 with real coefficients and the following zeros.

4 (multiplicity 2) . i

Answer 1

The polynomial f(x) is given by: f(x) = (x+4)²(x+i)(x-i)

To find a polynomial f(x) of degree 4 with real coefficients and zeros given as 4 with multiplicity 2 and i, you can use the factored form of a polynomial. The correct factored form should be:

`\[ f(x) = (x + 4)^2 \cdot (x + i) \cdot (x - i) \]`

This expression represents a polynomial of degree 4 because it has two factors of \(x + 4\) (multiplicity 2) and two distinct linear factors x + i and x - i. Additionally, the coefficients are real since both 4 and i are considered real numbers.

So, the correct answer is indeed
`\( f(x) = (x + 4)^2 \cdot (x + i) \cdot (x - i) \)`. If you expand this expression, you'll obtain a polynomial of degree 4 with real coefficients.