The equation of the quadratic function is f(x) = x²+ 2/3x - 1/9
<h3>How to determine the quadratic equation?</h3>
From the question, the given parameters are:
Roots = (-1 - √2)/3 and (-1 + √2)/3
The quadratic equation is then calculated as
f(x) = The products of (x - roots)
Substitute the known values in the above equation
So, we have the following equation
![f(x) = (x - \frac{-1-\sqrt{2}}{3})(x - \frac{-1+\sqrt{2}}{3})](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%28x%20-%20%5Cfrac%7B-1-%5Csqrt%7B2%7D%7D%7B3%7D%29%28x%20-%20%5Cfrac%7B-1%2B%5Csqrt%7B2%7D%7D%7B3%7D%29)
This gives
![f(x) = (x + \frac{1+\sqrt{2}}{3})(x + \frac{1-\sqrt{2}}{3})](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%28x%20%2B%20%5Cfrac%7B1%2B%5Csqrt%7B2%7D%7D%7B3%7D%29%28x%20%2B%20%5Cfrac%7B1-%5Csqrt%7B2%7D%7D%7B3%7D%29)
Evaluate the products
![f(x) = (x^2 + \frac{1+\sqrt{2}}{3}x + \frac{1-\sqrt{2}}{3}x + (\frac{1-\sqrt{2}}{3})(\frac{1+\sqrt{2}}{3})](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%28x%5E2%20%2B%20%5Cfrac%7B1%2B%5Csqrt%7B2%7D%7D%7B3%7Dx%20%2B%20%5Cfrac%7B1-%5Csqrt%7B2%7D%7D%7B3%7Dx%20%2B%20%28%5Cfrac%7B1-%5Csqrt%7B2%7D%7D%7B3%7D%29%28%5Cfrac%7B1%2B%5Csqrt%7B2%7D%7D%7B3%7D%29)
Evaluate the like terms
![f(x) = x^2 + \frac{2}{3}x - \frac{1}{9}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E2%20%2B%20%5Cfrac%7B2%7D%7B3%7Dx%20-%20%5Cfrac%7B1%7D%7B9%7D)
So, we have
f(x) = x²+ 2/3x - 1/9
Read more about quadratic equations at
brainly.com/question/1214333
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