Question

For the polynomial function ƒ(x) = x5 − x4 − 9x3 + 9x2, find the zeros. Then determine the multiplicity at each zero and state whether the graph displays the behavior of a touch or a cross at each intercept.

Answer 1

Give f(x) = x5 − x4 − 9x3 + 9x2, to obtain the zero we need to factorize the expression. This will give:
x(x+3)(x-1)(x-3)
thus the zeros will be:
x=-3
x=0
x=1
x=3