Question

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

Answer 1

`4`, `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(x)` becomes `0`.

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

Hence, zeros of `f(x)` are given by `(x+4)=0`, `(2x–1)=0`, and `(x–7)=0`, i.e. for `x=-4`, `x=1/2` and `x=7`.

Hence, `4`, `1/2` and `7` are zeros of `f(x)=(x+4)(2x–1)(x–7)`.