How do you find a polynomial function that has zeros x=5,1,2 and degree n=4?

1 Answer
Aug 10, 2018

f(x)=(x+5)2(x1)(x2)=x4+7x33x255x+50

Explanation:

If a polynomial function f(x) has zeros x=5, x=1 and x=2, then it has factors (x+5), (x1) and (x2).

If these were its only factors, then it would be a cubic.

It is not clear from the question whether 5, 1 and 2 are supposed to be the only zeros. If so then one of them must be of multiplicity 2.

In any case, a suitable quartic would be:

f(x)=(x+5)2(x1)(x2)=x4+7x33x255x+50