Answer: 1/2, 0, and -2
Given:
[tex]f(x)=2x^4+x^3-5x^2+2x[/tex]To know if a given value is a zero of a function, f(x) must be equal to 0. With this, we will substitute the given values and see which values will result in f(x)=0.
[tex]\begin{gathered} f(x)=2x^4+x^3-5x^2+2x \\ f(\frac{1}{2})=2(\frac{1}{2})^4+(\frac{1}{2})^3-5(\frac{1}{2})^2^{}+2(\frac{1}{2})=0 \\ f(0)=2(0)^4+(0)^3-5(0)^2+2(0)=0 \\ f(-1)=2(-1)^4+(-1)^3-5(-1)^2+2(-1)=-6 \\ f(-2)=2(-2)^4+(-2)^3-5(-2)^2+2(-2)=0 \end{gathered}[/tex]From these, we can see that the values 1/2, 0, and -2 resulted in f(x)=0. Therefore, the answers are 1/2, 0, and -2.
