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:
[tex]g(x)=(5x-1)(x+4)[/tex]
We need to find the solutions to the equation g(x)=0. So,
[tex]g(x)=0[/tex]
[tex](5x-1)(x+4)=0[/tex]
Using zero product property, we get
[tex]5x-1=0[/tex] and [tex]x+4=0[/tex]
[tex]x=\dfrac{1}{5}[/tex] and [tex]x=-4[/tex]
Therefore, the solutions to the equation g(x)=0 are [tex]x=\dfrac{1}{5}[/tex] and [tex]x=-4[/tex].
