Find the equation of the polynomial

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SUMMARY

The polynomial of degree 4 with zeros at -2, 2, 1, and 1, and a leading coefficient of 1 can be expressed as \( f(x) = (x + 2)(x - 2)(x - 1)^2 \). This formulation arises from the fact that the roots of the polynomial directly correspond to its factors. The polynomial can be expanded to yield \( f(x) = x^4 - 2x^2 - 4 \). Understanding polynomial roots and their corresponding factors is crucial in deriving the polynomial equation.

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Homework Statement


Find the equation of the polynomial of degree 4 with zero's at -2, 2, 1, 1 and a leading coefficient of 1.


Homework Equations


?


The Attempt at a Solution


I don't know how to attack this one, I'm sure if I could see how to do it I could do it myself byt my head isn't working right now. All I can gather from that information is the first bit is x ^ 4 - Which isn't much. I'm thinking I have to substitue the values for zero into an equation and solve simultaneously? Can anyone help?
 
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Noir said:
Find the equation of the polynomial of degree 4 with zero's at -2, 2, 1, 1 and a leading coefficient of 1.

Hi Noir! :smile:

Hint: factors :wink:
 

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