Find the zeros of each of the following functions f (y) =y^5-2y³+y​

y = 0, y = -1 (Multiplicity 2) and y = 1 Multiplicity 2)

Step-by-step explanation:

y^5 - 2y³ + y​ = 0

y(y^4 - 2y^2 + 1) = 0

So one zero is y = 0.

y^4 - 2y^2 + 1 = 0

(y^2 - 1)(y^2 - 1) = 0

(y - 1)((y + 1)(y - 1)(y + 1) = 0

so y = -1 (Multiplicity 2) and y = 1 Multiplicity 2).

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