Question

The factors of the quadratic function g(x) are (5x-1) and (x+4). What are the solutions to the equation g(x)=0?

Answer 1

Given:

The factors of the quadratic function g(x) are (5x-1) and (x+4).

To find:

The solutions to the equation g(x)=0.

Solution:

If the factors of the quadratic function g(x) are (5x-1) and (x+4), then the function is defined as:

$g(x)=(5x-1)(x+4)$

We need to find the solutions to the equation g(x)=0. So,

$g(x)=0$

$(5x-1)(x+4)=0$

Using zero product property, we get

$5x-1=0$ and $x+4=0$

$x=\dfrac{1}{5}$ and $x=-4$

Therefore, the solutions to the equation g(x)=0 are $x=\dfrac{1}{5}$ and $x=-4$.