What are the zeros of the function f(x) = x^2 – 2x^3?

Finding the Zeros of the Function f(x) = x² – 2x³

To find the zeros of the function f(x) = x² – 2x³, we need to set the function equal to zero and solve for x:

Step 1: Set f(x) to zero

Our equation becomes:

x² – 2x³ = 0

Step 2: Factor the equation

We can factor out the common term x²:

x²(1 – 2x) = 0

Step 3: Set each factor equal to zero

This gives us two possible factors to solve:

1. x² = 0
2. 1 – 2x = 0

For the first factor, x² = 0, we find:

x = 0

For the second factor, 1 – 2x = 0, we solve for x:

2x = 1
x = rac{1}{2}

Step 4: Conclusion

The zeros of the function f(x) = x² – 2x³ are:

• x = 0
• x = rac{1}{2}