To find the zeros of the function y = x^5 - 10x^3 + 9x, we need to set y equal to zero and solve for x.

0 = x^5 - 10x^3 + 9x

We can factor out an x from each term:

0 = x(x^4 - 10x^2 + 9)

Now we have a quadratic equation in terms of x^2. Let's set x^2 = y for simplicity:

0 = y^2 - 10y + 9

We can solve this quadratic equation by factoring:

0 = (y - 1)(y - 9)

Setting each factor equal to zero gives the solutions y = 1 and y = 9.

Remember that y = x^2, so we need to solve for x:

x^2 = 1 gives x = 1 and x = -1.
x^2 = 9 gives x = 3 and x = -3.

So, the zeros of the function are x = -3, -1, 0, 1, 3.

Question

To find the zeros of the function y = x^5 - 10x^3 + 9x, we need to set y equal to zero and solve for x.

0 = x^5 - 10x^3 + 9x

We can factor out an x from each term:

0 = x(x^4 - 10x^2 + 9)

Now we have a quadratic equation in terms of x^2. Let's set x^2 = y for simplicity:

0 = y^2 - 10y + 9

We can solve this quadratic equation by factoring:

0 = (y - 1)(y - 9)

Setting each factor equal to zero gives the solutions y = 1 and y = 9.

Remember that y = x^2, so we need to solve for x:

x^2 = 1 gives x = 1 and x = -1.
x^2 = 9 gives x = 3 and x = -3.

So, the zeros of the function are x = -3, -1, 0, 1, 3.

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