Write a polynomial function of least degree with real coefficients in standard form that has the given zeros. –2, –4, –3 + 4i

Given:

Zeroes of a polynomial are –2, –4, –3 + 4i.

To find:

The polynomial function of least degree with real coefficients in standard form.

Solution:

According to the complex conjugate root theorem, if a complex number a+ib is a zero of a polynomial, then its conjugate a-ib is also a zero of than polynomial.

–3 + 4i is zero of the polynomial. So, by complex conjugate root theorem -3-4i is also a zero of required polynomial.

If c is a zero of p(x), then (x-c) is a factor of p(x).

–2, –4, –3 + 4i, -3-4i are zeroes of the polynomials. So, (x+2), (x+4), (x+3-4i), (x+3+4i) are the factors of the required polynomial.

Let the required polynomial be p(x), so

Combining like terms, we get

Therefore, the required polynomial is .