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A polynomial function
f is defined as
f(x)=3(x-4)(2x-1). What is the product of all of the zeros of function
f ?

A polynomial function $f$ is defined as $f(x)=3(x-4)(2 x-1)$ . What is the product of all of the zeros of function $f$ ?

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Complex conjugate theorem

Full solution

Q. A polynomial function

f

is defined as

f(x)=3(x-4)(2 x-1)

. What is the product of all of the zeros of function

f

?

Identify Zeros: Identify the zeros of the polynomial function. $\newline$ The zeros of the polynomial function $f(x)$ are the values of $x$ that make the function equal to zero. To find these, we set each factor in the function equal to zero. $\newline$ $(x-4) = 0$ and $(2x-1) = 0$
Solve Equations: Solve for $x$ in each equation. $\newline$ For the first equation: $\newline$ $x - 4 = 0$ $\newline$ $x = 4$ $\newline$ For the second equation: $\newline$ $2x - 1 = 0$ $\newline$ $2x = 1$ $\newline$ $x = \frac{1}{2}$ $\newline$ We have found the zeros: $x = 4$ and $x = \frac{1}{2}$ .
Calculate Product: Calculate the product of the zeros. $\newline$ The product of the zeros is found by multiplying them together. $\newline$ Product = $4 \times \left(\frac{1}{2}\right)$
Perform Multiplication: Perform the multiplication to find the product. $\newline$ Product = $4 \times \left(\frac{1}{2}\right) = 2$

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