Write a Polynomial f(x) in complete factored form that satisfies the conditions: The leading coefficient is 10. The degree is 6. there is a zero at 2 with multiplicity 3, a zero at 6 with multiplicity 1 and a zero of 5i.
There is a zero at 2 with multiplicity 3
\(f(x) = (x-2)^3 (?)\)
A zero at 6 with multiplicity 1
A zero of 5i
It is good to note that complex factors come in pairs so by adding a complex factor you essentially solve for two complex zeroes
Now we have a polynomial with a degree of 6. However, we need the leading coefficient to be 10. To do this we just include a ten as a subset of the function like this. \(f(x)=10(x-2)^3(x-6)(x^2+25)\) Now you have a polynomial f(x) that satisfies all the given conditions.