# How do you find the zeros of the polynomial function with equation  f(x) = (x + 4)(2x – 1)(x – 7)?

Feb 22, 2016

$4$, $\frac{1}{2}$ and $7$ are zeros of f(x)=(x+4)(2x–1)(x–7).

#### Explanation:

Zeros of the polynomial function f(x)=(x+4)(2x–1)(x–7), are those values of $x$ for which value of $f \left(x\right)$ becomes $0$.

As $f \left(x\right)$ is a multiple of three linear functions $\left(x + 4\right)$, (2x–1), and (x–7), $f \left(x\right)$ if any of these three linear function is equal to zero.

Hence, zeros of $f \left(x\right)$ are given by $\left(x + 4\right) = 0$, (2x–1)=0, and (x–7)=0, i.e. for $x = - 4$, $x = \frac{1}{2}$ and $x = 7$.

Hence, $4$, $\frac{1}{2}$ and $7$ are zeros of f(x)=(x+4)(2x–1)(x–7).