y = x5 − 10x3 + 9x(a) Find the zeros algebraically. (Enter your answers as a comma-separated list. If there are no real zeros, enter DNE.)
Question
Solution 1
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
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