Problem

What are the zeros of the equation $y+100 x=x^{3}$ ?

Answer

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Answer

Final Answer: The zeros of the equation $y+100 x=x^{3}$ are \(\boxed{-10, 0, 10}\).

Steps

Step 1 ：Set the equation $y+100 x=x^{3}$ equal to zero to find the zeros of the equation.

Step 2 ：Since we are looking for the zeros of the equation, we can set y = 0. This gives us the equation $x^{3} - 100x = 0$.

Step 3 ：Factor out an x from the equation to get $x(x^{2} - 100) = 0$.

Step 4 ：This equation has solutions when x = 0 or when $x^{2} - 100 = 0$.

Step 5 ：Solving the second equation gives us two more solutions, x = 10 and x = -10.

Step 6 ：Therefore, the zeros of the equation are x = 0, x = 10, and x = -10.

Step 7 ：Final Answer: The zeros of the equation $y+100 x=x^{3}$ are \(\boxed{-10, 0, 10}\).

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