Question

Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree​ 5; ​ zeros: -1; −i; −7+i

Answer 1

To form a polynomial with real coefficients and the given zeros, we can use the fact that the complex zeros occur in conjugate pairs. By substituting the zeros into the polynomial formula, we can form the polynomial of degree 5.

Step-by-step explanation:

To form a polynomial with real coefficients, we need to consider the given zeros which are -1, -i, -7+i. Since -i is a zero, its conjugate i will also be a zero. So we have the following zeros: -1, -i, i, -7+i.

A polynomial of degree 5 will have 5 roots. So we can express the polynomial as:

f(x) = (x - (-1))(x - (-i))(x - i)(x - (-7+i))(x - (-7-i))

Simplifying further gives:

f(x) = (x + 1)(x + i)(x - i)(x - 7 + i)(x - 7 - i)