Functions and degrees

Question

Find a polynomial function of degree 3 with the given numbers as zeros. -1/3,0,5

Could you explain how to work these types of problems? Thanks!

Answer 1

Sure--it's easy. If I tell you, then you should always be able to work such a problem on your own, from now on.

 

Just imagine that you know the polynomial in factored form: f(x) = a(x-root#1)(x-root#2)...(x - root # n).

 

They have given you the roots, so your answer (for n=3) is the cubic f(x) = (x-0(x-5)(x-(-1/3)).

 

In this case, you can choose a = 3 & distribute it over the last factor, so a good final answer is

f(x) =x(x-5)(3x+1).