Problema Solution
Form a polynomial f(x) with real coefficients having the given degree and zeros
Degree: 3 zeros: -4 and 3-2i
Answer provided by our tutors
If a is a root of a polynomial, then (x – a) is a factor.
For polynomials with real coefficients, complex roots occur in conjugate pairs so, since 3-2i is a root then 3+2i is also a root
The polynomial is:
f(x) = (x – 3)(x -(3-2i))(x – (3+2i))
f(x) = = (x – 3)(x - 3 + 2i)(x - 3 - 2i)
f(x) = x^3 - 9x^2 +31x - 39