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

Posted 6 months ago

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.

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