Question

I don’t seem to get these right, I’m afraid I need a whole explanation.

Answer 1

EXPLANATION:

We are given the polynomial function;

$f(x)=2x^5-5x^3+12$

A zero of a function is a factor of that function such that when used as the input value results in zero.

To illustrate;

If

$(x-1)$

is a factor of a function, then;

$x=1$

Means when 1 is inputed into the function the function results into zero.

We shall take the options one after the other to determine which is not a zero of the function;

$\begin{gathered} For; \\ x=\frac{5}{2} \\ f(x)=2(\frac{5}{2})^5-5(\frac{5}{2})^3+12 \end{gathered}$$=2(\frac{3125}{32})-5(\frac{125}{8})+12$$\frac{3125}{16}-\frac{625}{8}+12$$\frac{3125}{16}-\frac{1250}{16}+12$$\frac{1875}{16}+12\ne0$

ANSWER:

This means 5/2 is not a possible zero of this polynomial