Question

What are the roots of the following function? f(x) (4x-1)(x+9)
please answer due today.
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Answer 1

`x=-9, \quad x=(1)/(4)`

Explanation:

Given function:

`f(x)=(4x-1)(x+9)`

The roots of a function are the x-values for which the function equals zero. Therefore, to find the roots, set the function to zero and solve for x.

Set the function to zero:

`\implies f(x)=0`

`\implies (4x-1)(x+9)=0`

Zero Product Property

If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Apply the zero product property:

`(4x-1)=0 \implies x=(1)/(4)`

`(x+9)=0 \implies x=-9`

Therefore, the roots of the given function are:

`x=-9, \quad x=(1)/(4)`