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smmscn's Question
Math
Posted 2 months ago

1. Find the zeros of the polynomial function
f(x)=x42x3+4x28x
f(x)=x^{4}-2 x^{3}+4 x^{2}-8 x
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Answer from Sia
Posted 2 months ago
Solution by Steps
step 1
To find the zeros of the polynomial function f(x)=x42x3+4x28xf(x) = x^4 - 2x^3 + 4x^2 - 8x, we start by factoring out the common term xx
step 2
Factor out xx from the polynomial: x(x32x2+4x8)=0x(x^3 - 2x^2 + 4x - 8) = 0
step 3
Set each factor equal to zero: x=0x = 0 and x32x2+4x8=0x^3 - 2x^2 + 4x - 8 = 0
step 4
Solve the cubic equation x32x2+4x8=0x^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 x32x2+4x8=0x^3 - 2x^2 + 4x - 8 = 0 are x=2x = 2 and x=±2ix = \pm 2i
step 6
Combine all the roots: x=0x = 0, x=2x = 2, and x=±2ix = \pm 2i
Answer
The zeros of the polynomial function f(x)=x42x3+4x28xf(x) = x^4 - 2x^3 + 4x^2 - 8x are x=0x = 0, x=2x = 2, and x=±2ix = \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 xx that make each factor equal to zero.

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