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.

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Mathematics

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19 July, 17:09

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.

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Clarence Holmes · 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