1. Find the zeros of the polynomial function
$$
f(x)=x^{4}-2 x^{3}+4 x^{2}-8 x
$$

Question

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the zeros of the polynomial function $f(x) = x^4 - 2x^3 + 4x^2 - 8x$, we start by factoring out the common term $x$. ‖ ‖ step 2 ⋮ Factor out $x$ from the polynomial: $x(x^3 - 2x^2 + 4x - 8) = 0$. ‖ ‖ step 3 ⋮ Set each factor equal to zero: $x = 0$ and $x^3 - 2x^2 + 4x - 8 = 0$. ‖ ‖ step 4 ⋮ Solve the cubic equation $x^3 - 2x^2 + 4x - 8 = 0$. This can be done by finding the roots of the cubic polynomial. ‖ ‖ step 5 ⋮ Using the Asksia-LL calculator result, the roots of the cubic polynomial $x^3 - 2x^2 + 4x - 8 = 0$ are $x = 2$ and $x = \pm 2i$. ‖ ‖ step 6 ⋮ Combine all the roots: $x = 0$, $x = 2$, and $x = \pm 2i$. ‖ ∻Answer∻ ⚹ The zeros of the polynomial function $f(x) = x^4 - 2x^3 + 4x^2 - 8x$ are $x = 0$, $x = 2$, and $x = \pm 2i$. ⚹ ∻Key Concept∻ ⚹Finding the zeros of a polynomial function⚹ ∻Explanation∻ ⚹To find the zeros of a polynomial function, factor the polynomial and solve for the values of $x$ that make each factor equal to zero.⚹◊What is the formal definition of the zeros of a polynomial function?⍭ Generate me a similar question◊

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