Find Functions with Given Zeros
√2, -√2, 3
find zero;s(x-3)(x-sqrt 2)(x+sqrt 2) = 0
(x-3)(x^2-2) = 0
x^3 -3 x^2 -2 x + 6 = 0
so
y = f(x) = x^3 -3 x^2 -2 x + 6
To find functions with the given zeros, we need to create a polynomial equation where the zeros are the roots.
Let's start with the first zero, √2. A function with this zero could be (x - √2) = 0.
Next, let's consider the second zero, -√2. A function with this zero could be (x + √2) = 0.
Finally, let's move on to the third zero, which is 3. A function with this zero could be (x - 3) = 0.
To find a function that has all three of these zeros, we need to multiply these factors together.
So, the polynomial function with these given zeros is f(x) = (x - √2)(x + √2)(x - 3).
Expanding this equation gives us f(x) = (x^2 - 2)(x - 3).
Hence, the function f(x) with the given zeros √2, -√2, and 3 is f(x) = (x^2 - 2)(x - 3).