Help please! :( Form a polynomial f(x) with real coefficients having the given degree and zero. Degree: 4; zeros: 4+5i; 5 multiplicity 2

Question

whpalmer4 · Answer

"with real coefficients" is a key term here: it means that $4+5i$ is not your only complex zero, but that you also need $4-5i$ as a zero.

"5 multiplicity 2" means that you have two terms that equal 0 when x = 5, not just one.

whpalmer4 · Answer

do you know how to construct a polynomial from a list of zeros?

if your zeros are $z_1,z_2, ...,z_n$, the polynomial is $$P(x) = a(x-z_1)(x-z_2)...(x-z_n)$$where $a$ is a scaling factor and can be set to equal 1, or a different value if you need the polynomial to pass through a specified point.

whpalmer4 · Answer

The tricky part is expanding the polynomial after writing the factored form.

anonymous · Answer

Yes, my problem was multiplying f(x) and combining like terms. It is a bit confusing. I am still trying though.