Find an equation of a polynomial function of degree 5 with integer coefficients with zeros 0, -2, and 1/2.
To find an equation of a polynomial function with the given zeros, we need to use the fact that if a number, let's call it "a," is a zero of a polynomial function, then (x - a) is a factor of that polynomial.
Given that the zeros are 0, -2, and 1/2, we can write the factors as follows:
(x - 0), (x - (-2)), and (x - 1/2).
Simplifying the factors, we get:
(x - 0), (x + 2), and (x - 1/2).
Now, to find a polynomial function of degree 5 with integer coefficients, we need to multiply these factors together. Since we have three factors, the degree of the polynomial will be 3.
Multiplying the factors, we get:
(x)(x + 2)(x - 1/2).
Expanding this expression gives us:
(x)(x^2 + 2x - x - 1) = (x)(x^2 + x - 1).
Finally, we can distribute the x term:
x^3 + x^2 - x.
So, an equation of a polynomial function of degree 5 with integer coefficients and zeros 0, -2, and 1/2 is:
f(x) = x^3 + x^2 - x.