Construct a polynomial function with the following properties: fifth degree, 4 is a zero of multiplicity 2, -3 is the only other zero, leading coefficient is 4.

Question

anonymous · Answer

do you know what "multiplicity" means in this context?

anonymous · Answer

Not really

anonymous · Answer

if $a$ is a zero of $p(x)$ of multiplicity $n$ then $p(x)$ has a factor of $(x-a)^n$

anonymous · Answer

for example, if $4$ is a zero of multiplicity 2, then the polynomial has a factor of $(x-4)^2$ to bring it more down to earth (and also answer your question)

anonymous · Answer

at least partially answer it
since the other zero is $-3$ there is a factor of $(x+3)$

anonymous · Answer

So do I multiply (x+3)(x-2)^2 and then 4 in order to get 4x^5?

helder_edwin · Answer

u r close. it should be
$$\large f(x)=4\cdot(x+3)^n(x-4)^2 $$
in order to get a polynomial of degree 5, what should be the value of n?

anonymous · Answer

3

anonymous · Answer

Correct?

helder_edwin · Answer

yes

anonymous · Answer

Thanks helder_edwin

helder_edwin · Answer

u r welcome